Question

Construct an angle of ${90}^{\circ }$ at the initial point of a given ray and justify the construction.

Answer 1

1. Draw a ray $OB$.

2. Cut an arc from point $O$ of any length (as shown in the fig).

3. Cut two arcs $Q$ and $R$ on the previous arc with same radius. (which are at the angle of ${60}^{\circ }$ and ${120}^{\circ }$).

4. Draw two arcs from points $Q$ and $R$ and their point of intersection is $S$.

5. Join $O$ and $S$.

Hence, $\angle SOP$ is ${90}^{\circ }$