Learning

If you’d like to learn how to confidently find out the size of a wide variety of angles, in different shapes, simply continue reading to discover how to find out the size of most common angles. As an example, you’ll be able to figure out how to find out the value of an angle in a right angled triangle.

How to find the measure of the indicated angle:

1. How to find out the size of an angle in a right angled triangle

To start off with, it’s a great idea to learn how to figure out the easiest angle in geometry, a right angled triangle. To be able to accurately work out a mystery angle in a right angle triangle, you need to know the length of two of your triangle’s three sides.

The three sides of a triangle are named the adjacent angle, which is located adjacent to the angle, the opposite angle and the hypotenuse. It doesn’t matter which two sides you have the measurements of as long as you know the length of two of the three sides which make up your right angled triangle.

The next step which you have to take the figure out your angle is to decide whether to use sine, cosine or tangent. Use sine or sin if you know the lengths of your opposite side and your hypotenuse side. Use cosine if you have the measurements of your adjacent side and your hypotenuse side and if you have opposite side and your adjacent side you’ll need to use tangent.

Once you’ve figured out to use sine, cosine or tangent you’ll ned to use the corresponding formula. As an example if you need to use the sine equation, use the equation Sin (x) = opposite length multiplied by hypotenuse angle = your answer.

A faster way to find out the angle inside a right angled triangle:

If you have a scientific calculator you can save yourself time by using your calculator to perform your equation as scientific calculators have cos, tan and sin buttons.

Tips on how to find angles in a triangle:

If you already know two angles within a triangle, you should be able to figure out the value of the remaining angle without using an algebraic formula. Even if you only know the value of one angle within a triangle, you may be able to figure out the value of the remaining angle, by using the rules below.

1. All the angles within a triangle always add up to 180 degrees.

So if you know two angles within a triangle, simply add both the angles which you have together and subtract them from 180 degrees, to find out the size of your remaining angle.

2. Opposite angles always equal 360 degrees.

If you know the opposite angle within a triangle, you also know how large your mysterious angle is.

Hopefully you now have a few ideas of how you can find out the size of an unknown, mysterious angle in a regular triangle.

If you’re interested in learning a few basic algebra formulas, continue reading on to discover some of the most useful basic algebra formulas to learn.

The most useful algebra formulas to learn:

1. The difference between two squares

The difference between two squares refers to when two binomials have only one difference, when one term features a plus and the other term features a minus sign. To quickly discover the difference between two squares use the following basic algebra formula (x+y) (x-y) = x squared – y squared.

2. The difference of cubes

To figure out the difference of cubes use the formula a to the power of 3 – b to the power of 3 = (a-b) (a+b).

3. The sum of cubes

If you need to find out the sum of cubes, the formula which you should use is a to the power of 3 + b to the power of 3 = (a+b) (a squared -ab + b2).

4. The pythagorean theorem

The pythagorean theorem is one of the most commonly used algebraic equations and is used to accurately figure out the lengths and sides of a right angled triangle. Thankfully the pythagorean theorem equation is one of the simplest algebraic equations to learn.

When a and b refer to the two sides of a triangle which stem from either side of a triangle’s right angle use the equation a squared plus b squared = c squared. In this equation c, refers to the the side which you’re trying to work out the value of, which is known as the hypotenuse.

5. How to multiply powers which boast the same base

To multiply powers which feature the same base make sure to add your exponents. The formula which you should use to multiply powers which boast the same base is x to the power of a, x to the power of b = x to the power a+b.

Before you try to figure out a trickier algebraic problem such as this particular problem, you may be better off learning simpler equations such as the pythagorean theorem. Which is much easier to grasp and will give you a solid base to learn more difficult algebraic equations.

6. How to raise a power

If you’re unsure of how to raise a power, simply use the formula (X to the power of a) to the power of b = X to the power of ab. Just remember that when you need to raise a power by a power to multiply your exponents.

7. How to discover the power of a product property

To workout the power of a product property use the algebraic formula (xy) to the power of a = x to the power of a, y to the power of a. Also make sure that when you raise a product to a power to find out the power of each factor, in order to multiply your factors.

So if you haven’t looked at an algebra book since high school and you’re looking to brush up on your algebra skills, it’s well worth starting off with mastering the simple formulas listed above.

To construct a 135-degree angle you need basic tools you find in your mathematics geometrical set.

For this project we need the following tools;

1. a protractor

2. a 15 cm ruler

3. a compass

4. a pencil and rubber

This is how to construct a 135-degree angle using the above tools. O’Neill’s Green Services also use these methods in constructing 135-degree angle making paves and turfs

METHOD 1

The first steps to constructing a 135-degree angle are constructing a right angle first (90 degrees angle)

1. using your ruler draw a straight line and name the ends O and B

Now you have to create intersecting arcs using the following instructions

1. Open your compass to any radius, using O as your center, draw an arc to cut line OB, and name the point of meeting X

2. Do not change the radius of the compass you used in step 1 above, using X as your center, draw another arc to cut the first arc and name that point D

3. Without changing the radius of your compass, this time place your compass at point D, draw another arc to cut your first arc and name that point C

4. Keeping the radius of your compass constant as the steps 1, 2 and 3 above, place your compass at point D and draw an arc, repeat the step placing your compass at point C and draw an arc to cut the arc you just drew. Name this point E.

5. Using a ruler draw a line from point E to point O, extend OE to a point A. the angle AOB you have just formed is a 90-degree angle

6. Extend line BO to your left and name the point Z, since this is a straight line, the angle AOZ formed is also a straight equivalent to 90 degree

PART B.

For this part, we now construct a 135 degree by splitting angle AOB into 2 equal parts.

7. Using a compass open it to a radius of your choosing, using O as your center, draw an arc to cut the line OB and AO at point P and Q respectively

8. Now using your compass set at the same radius as step 7 above, place the compass at point Q and draw an arc, place the compass at point P without changing the radius and draw an arc to cut the arc you just drew and name that point F

9. Using your ruler join point F to O and extend the line to point G.

Observation

– Angles GOB and AOG are both equal to 45 degree

– Adding right angle ZOA (90 degrees) with angle AOG

90+45 = 135

Therefore angle ZOG is a 135-degree angle

METHOD 2

1. Draw a line using your ruler and name the ends A and B

2. Find the center of your line using the ruler, for example; assuming your line AB measures 6 inches, your center is at the 3-inch mark. Name this point O.

3. Now place your protractor aligned to line AB, make sure the center of the protractor is at point O.

4. Find the 135-degree mark on the protractor, mark it with a dot and name it C

5. Join CO with a straight line

6. The angle AOC is a 135-degree angle

If you’re interested in finding out detailed facts and formulas which relate to two common types of prisms, rectangular prisms and triangular prisms, simply continue reading to discover a simple guide to understanding both types of prisms.

How many sides does a rectangular prism have:

A rectangular prism has six sides or faces, all of which are rectangles. Hence the name rectangular prism.

What are some fascinating facts about rectangular prisms:

1. All the angles in a rectangular prism are right angles. No matter how small or large a rectangular prism happens to be.

2. Common every day examples of rectangular prisms include rectangle buildings and rectangle boxes.

3. If you were to slice the length of a rectangular prism at any point, the shape which you’d slice would be exactly the same shape and size as if you were to slice your rectangular prism at another point.

How to find the volume of a rectangular prism:

To find out the volume of a rectangular cuboid, you can use a standard formula to find out the volume of a cuboid as a rectangular prism is a type of cuboid.

Simply multiply the length of your rectangular prism by the width of your prism and the height of your rectangular prism.

How to find the surface area of a rectangular prism:

If you need to work out the surface area of a rectangular prism, you can use the formula A = 2wl + 2lh + 2hw. In this formula A = surface area, w = width, l = length and h = height.

How many faces does a triangular prism have?

A triangular prism features five faces and also boasts 9 edges and 6 vertices. A common example of a triangular prism is a Toblerone chocolate bar.

How to find the height of a triangular prism:

One formula which you can use to accurately find out the height of a regular triangular prism is SA = 2B + Ph. In this formula SA = surface area, B = the area of your prism’s base, P = the perimeter of your prism’s base and h = the height of your prism.

To be able to use this particular formula to work out the height of your triangular prism you’ll need to know the surface area of your triangular prism as well as the length of each side of your triangular prism’s base and the area of your triangular prism’s base.

How to work out the surface area of a triangular prism:

It’s a little tricker to work out the surface area of a triangular prism than to simply find the height of a triangular prism. To work out the surface area of a triangular prism you’ll need to use the formula 3 andndash; a andndash; (a + h). In this particular formula a = area and h = height.

In conclusion, hopefully you found the facts and formulas about rectangular prisms and triangular prisms which were presented above informative and now have a better understanding about both types of common, regular prisms. Both of which are commonly found in everyday life, so you may find the formulas listed above useful.

If you’re interested in learning about the features of a few common types of polygons such as octagons and decagons, simply continue reading to get started.

What is a 10 sided polygon called? If you were trying to find what a 10 sided polygon is called. A 10 sided polygon is simply referred to as a decagon.
What are some interesting facts about decagons?Regular decagons have 10 even sides, which are always equal in length. The angles inside a regular decagon happen to equal 144 degrees, no matter how small or large a regular decagon is. An example of a decagon which doesn’t have equal sides is a quasi regular decagon which alternates between two different types of edges. If you’re interested in the symmetry order of polygons, a regular decagon has a symmetry order of 20.
What is a 9 sided polygon called?
The answer which you’re looking for is nonagon.

What are some interesting facts about nonagons?
Nonagons have 9 sides and 9 vertices and the internal angles inside of a nonagon measure as 140 degrees. A real life example of a nonagon structure is the US Steel Tower, which is an irregular nonagon. While all Baha’i Temples are also required to be built to be nonagons. An alternative name for a nonagon is enneagon.
What is an 8 sided polygon called?
The answer is an octagon. One easy way to remember that an octagon has 8 sides is that the root of the world octagon, translates to the number 8, which is why an octopus, which has 8 legs has the same root oct, which means 8.
Are there any interesting facts about octagons?
As you may have guessed regular octagons have eight sides of an even length and feature 8 vertices. Another interesting fact about octagons is that you can create an irregular regular octagon as a quasi regular truncated square which features two district styles of edges. An example of a real life octagon is a UFC, mixed martial arts ring, which is shaped as a regular octagon and has 8 even sides and 8 vertices.
What is a 7 sided polygon called?
A 7 sided polygon can be referred to either as a heptagon or a septagon. However, the most common term that you’ll come across is defintely heptagon.
What are some interesting facts about heptagons?
As you may have guessed they are comprised of 7 equal sides and features 7 vertices each of which boast the same interior angles, which equates to 128.57 degrees. simple to find out the area of a regular heptagon. To find out the area of a regular heptagon you’ll need to use the formula 1/2 multiplied by the perimeter multiplied by the apothem.
What is a 6 sided polygon called?
The answer is a hexagon. The root of the word hexagon, hex translates to the number six in Greek.
What are a few interesting facts about hexagons?
Yes, regular hexagons are made up of six equal sides and also feature six vertices. Some properties of regular hexagons include that regular hexagons are convex, cyclic, isogonal and isotoxal. Hopefully, you learned a few brand new facts about a few common polygons such as decagons and octagons.

If you’re interested in discovering some of the key features of polygons, continue reading to discover a simple, clear guide to understanding polygons.

What is a polygon?

A polygon is a two dimensional shape, which is comprised of straight lines. Any two dimensional shape which is curved such as a circle is not referred to as a polygon. Other examples of shapes which are not polygons include open shapes, which are not fully enclosed as well as three dimensional shapes such as a cube, a sphere or a pyramid.

What are the differences between regular polygons and irregular polygons:

A polygon with all sides and angles and congruent is classed as a regular polygon while a polygon which features sides of varying lengths and angles is referred to as an irregular polygon.

An example of a regular polygon is an equilateral triangle which is comprised of three sides which are equal in length as well as equal interior angles which each add up to 60 degrees. While a common example of a irregular polygon is a scalene triangle which features three sides of varying lengths and which has interior angles of varying different sizes.

What is a concave polygon?
A concave polygon is a polygon which features at least one angle which is at least 180 degrees.
What is a convex polygon?
Unlike a concave polygon a convex polygon will not have a single interior angle which is larger than 180 degrees.
What is a complex polygon?
If you’ve never come across the term complex polygon, a complex polygon is a polygon which has a line which crosses another line.
What are some common examples of polygons:
One of the most common types of polygon are quadrangles. Quadrangles all have four sides and include simples squares and rectangles as well as rhombuses. Furthermore every quadrangle polygon has interior angles which add up to 360 degrees. Quadrangles can also be referred to as parallelograms. Parallelograms feature opposite sides which are always equal in length.
Triangles are another example of a polygon. There are three different types of polygons, equilateral triangles feature three sides of equal lengths, isosceles triangles feature two even sides and one uneven side and feature two, not three equal angles. Finally scalene triangles boast three sides which are all different in length.
Other examples of polygons which you may come across in everyday life include pentagons, hexagons and octagons. Pentagons have five sides, hexagons have six sides and octagons have eight sides.
How to accurately calculate the area of a quadrangle:
To effortlessly figure out the area of a quadrangle, such as a square or a rectangular, multiple the length of your chosen polygon with the vertical height of your quadrangle. Working out the area of a quadrangle couldn’t be easier.
How to calculate the area of other types of polygons;
If you’d like to figure out the area of a polygon which isn’t a quadrangle, you’ll need to split up your polygon into equal triangles before using an algebaric equation to find your answer.
Hopefully, you’re now feeling more confident about your knowledge of a wide variety of polygons.

In order to learn everything which you need to know about triangular prisms, simply continue reading to discover a simple guide to triangular prisms.

What is a triangular prism:

A triangular prism is essentially a three sided prism that is comprised of even sized rectangular prisms. The base shape of a triangular prism is a traditional triangle. A triangular prism is comprised of 2 triangular shapes and three rectangular shapes. The two ends of a triangular prism are always parallel to each other, while the four side faces of a triangular prism are rectangular parallelograms.

Furthermore triangular prisms are three dimensional as all shapes which are prisms are three dimensional shapes as opposed to a simple, two dimensional shape such as a square or an octagon. Another example of a prism is a sphere with is three dimensional, unlike a circle which is two dimensional.

What is a right triangular prism:

The term right triangular prism refers to a triangular prism which has a triangular base which edges and face are all perpendicular to the base edges.

Are there any examples of triangular prisms that are easily recognisable:

An example of a triangular prism which you may have seen in real life is an oversized Toblerone chocolate box, which you’ll find sold in the duty free section of most international airports around the world. Some other examples of triangular prisms which you may have come across include camping tents and triangular rooves.

What is a prism:

To understand wha ta triangular prism is, it’s essential to ensure that you’re clear about what a prism is. A prism has identical ends and flat faces and boasts the same exact cross section along its length. So if you were to cut a prism along its length in two different areas, the slices that you’d get would look exactly the same. Furthermore prisms always feature flat sides are are never curved like a cylinder.

How many vertices does a triangular prism have?

Triangular prisms have six vertices. Vertices being corners.

How many faces does a triangular prism have?

A triangular prism always has five congruent faces.

How many edges does a triangular prism have?

A triangular prism has nine edges.

How to calculate the volume of a triangular prism:

If you’re curious about how to accurately calculate the volume of a triangular prism, simply follow the following mathematical equation. Multiply the base of your triangular prism by its height.

How to calculate the surface area of a triangular prism accurately:

In order to figure out the surface area of a triangular prism use the equation 2A + PH. In this formula A = your base area, P = the perimeter of your triangular prism and H refer to the height of your prism.

What is a semi-regular triangular prism?

If you’ve heard the term semi-regular triangular prism and are wondering how a semi-regular triangular prisim differs from a regular triangular prism, a semi-regular triangular prism features an equilateral triangle and several square faces.

Hopefully, you now fully understand the basic facts about triangular prisms.

If you’re curious about what a ten sided polygon is and how to correctly identify one, simply continue reading to discover everything which you need to know about ten sided polygons.

What is a ten sided polygon?

A ten sided polygon is a regular polygon which is referred to as a decagon. A decagon is a two dimensional shape. If you continue reading you’ll discover some of the key differences between the two different types of decagons which exist regular decagons and irregular decagons as well as a few simple mathematical equations that can be applied to regular decagons .
How many edges and vertices does a regular decagon have?

All decagons have 10 edges and vertices. All of which are even in length and size. If it’s been awhile since you’ve come across the term vertices, the term simply refers to the individual points at which each side in a shape such as a regular decagon meet.

How many degrees does the internal angle of a regular decagon add up to?

As regular decagons boast sides which are all uniform in size and length, the internal angle of each internal angle of a regular decagon always adds up to 144 degrees.

What are some of the key properties of a regular decagon?

A polygon is a convex shape as each internal angle in a regular decagon is less than 180 degrees. As just stated above each internal angle in a regular decagon always adds up to 144 degrees. Furthermore, regular decagons can also be referred to as being equilateral polygons as regular decagons have even sides and vertices.

How to find the area of a regular decagon:

If you ever need to find the area of a regular decagon simply use the following mathematic equation. Area equals half multiplied by perimeter multiplied by apothem. In order to get your answer.

How to find the perimeter of a regular decagon:

In order to find out the perimeter of a regular decagon simply multiply sides by ten in order to find the answer which you’re looking for.

Are all decagons regular decagons?

No, while most decagons which you’ll come across will probably be regular decagons, irregular decagons also exist. As long as a two dimensional shape features ten sides and is fully enclosed a shape can be accurately referred to as a 10 sided polygon or a irregular decagon. Like a regular decagon a irregular decagon will also have 10 equal congruent vertices and angles.

What properties does an irregular decagon feature?

An irregular decagon is concave because its angles are larger than 180 degrees, while the angles of a decagon are smaller than 180 degrees, which makes regular decagons convex.

Are they are mainstream examples of an irregular decagon?

If you’re having difficulty imagining what an irregular decagon may look like, one of the simplest most popular examples of an irregular decagon is a traditional star. If you look at a traditional star, you’ll notice that it’s an enclosed, two dimensional shape which features 10 sides and 10 vertices.

Hopefully, you now have a clear idea about what a 10 sided polygon is as well as the two different types of 10 sided polygons or decagons that exist.