Question

Using ruler and compasses only , construct angle of measure ${45}^{\circ }$.

Answer 1

Step 1. To construct an angle of measure first we have to construct an angle $\angle BAW=90°$.(Or we can choose any other terms for the angle)

Step 2. As we know that ${45}^{\circ }$ is half of ${90}^{\circ }$ so lets bisect bisect $\angle BAW$. For that taking $P$ and $T$ as centre draw arcs in between the right angle.These arcs will intersects at a point say point $U$.

Step 3. Now join $A$ and $U$ and produce to $V$. This $AV$ is the angle bisector of the angle $\angle BAW$. Thus $\angle BAV=45°$.