Edited by Kalpit, WanderWoman

This article teaches you how to construct a 45^o angle using a compass and a straightedge by different methods.

1
Mark the vertex of your angle anywhere on the paper. Let us name this point as M.

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2
Draw a ray MN, extending in any direction and of any length. This will be one of the arms of our angle.
3
Drop a perpendicular to the ray MN at any randomly chosen point (say X) on it.
4
Set width of your compass equal to the distance MX. Retain this width for the following step.
5
Place tip of the compass on X and draw an arc so as to cut the perpendicular at some point (say Y).
6
Connect the points M and Y with a straight line and extend it to form a ray ML.
- Angle LMN measures 45^o. Erase any extraneous constructions if you so wish.

1
Construct a 90^o angle.
2
Bisect the 90^o angle.
- Upon bisection, you'll be left with two angles, each measuring 45^o.
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