Question

Construct an angle of ${45}^{\circ }$ from a horizontal line and justify the construction.

Answer 1

1. Draw a ray $OX$.

2. Cut an arc from point $O$ of any length.

3. Cut two arcs $A$ and $B$ on the previous arc (which are at the angle of ${60}^{\circ }$ and ${120}^{\circ }$).

4. Cut two arc from points $A$ and $B$ and their point of intersection is $C$.

5. Join $O-C$. $\angle COX$ is ${90}^{\circ }$.

6. Bisect $\angle COX$ through cutting two arcs from $D$ and $E$, their point of intersection is $F$.

7. Join $F-O$,$\angle FOX$ is ${45}^{\circ }$