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