Question

Construct angles of following measures using ruler and compasses.
${60}^o$

Answer 1

We know that the angles in an equilateral triangle are all ${60}^{\circ }$ in size. This suggests that to construct a ${60}^{\circ }$ angle we need to construct an equilateral triangle as described below.

Step $1:$ Draw the arm $PQ$.

Step $2:$ Place the point of the compass at $P$ and draw an arc that passes through $Q$.

Step $3:$ Place the point of the compass at $Q$ and draw an arc that passes through $P$. Let this arc cut the arc drawn in Step $2$ at $R$.

Step $4:$ Join $P$ to $R$ .The $\angle QPR={60}^{\circ }$ as the $△PQR$ is equilateral triangle