Question

For constructing an angle of ${75}^{\circ }$

Steps of construction are:
Step 1: Draw ray AB
Step 2: Construct $\angle BAC={60}^{\circ }$
Step 3: Construct $\angle BAD={90}^{\circ }$
Step 4 will be

Answer 1

We know that
${75}^{\circ }={60}^{\circ }+{15}^{\circ }$
We have already constructed ${60}^{\circ }$
and ${15}^{\circ }$ is obtained by bisecting ${30}^{\circ }$

So next we construct ${90}^{\circ }$ since ${90}^{\circ }-{60}^{\circ }={30}^{\circ }$.

This ${30}^{\circ }$ is bisected to get ${15}^{\circ }$ so that
${60}^{\circ }+{15}^{\circ }={75}^{\circ }$

Therefore, Step 4 will be to bisect $\angle CAD$.