Question

Construct angles of following measures using ruler and compasses.
${90}^o$

Answer 1

We can construct a ${90}^{\circ }$ angle either by bisecting a straight angle or using the following steps.

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

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

Step $3:$ Place the point of the compass at $Q$ and draw an arc of radius $PQ$ that cuts the arc drawn in Step $2$ at $R$.

Step $4:$ With the point of the compass at $R$, draw an arc of radius $PQ$ to cut the arc drawn in Step $2$ at $S$.

Step $5:$ With the point of the compass still at $R$, draw another arc of radius $PQ$ near $T$ as shown.

Step $6$: With the point of the compass at $S$, draw an arc of radius $PQ$ to cut the arc drawn in step $5$ at $T$.

Step $7:$ Join $T$ to $P.\angle APT$ is ${90}^{\circ }$.