How to construct a 135 degree angle

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

Constructing a 135-degree angle is a straightforward process that enhances your geometry skills. With the right tools and techniques, you can achieve precise angles for various projects. Don’t forget to practice measuring angles to improve your accuracy in future tasks. For those curious about measurements, learning how to measure a ball can also be a useful skill.