Question

Construct the angle of ${30}^o$ using a ruler and compass.

Answer 1

So, to construct an angle of ${30}^{\circ }$, first construct a ${60}^{\circ }$ angle and then bisect it. For this, we would apply the following steps:

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 cuts the arc drawn in Step 2 at $R$.

Step 4: With the point of the compass still at $Q$, draw an arc near $T$ as shown.

Step 5: With the point of the compass at $R$, draw an arc of the same measure to cut the arc drawn in Step 4 at $T$.

Step 6: Join $T$ to $P.$ The angle $QPT$ is ${30}^{\circ }$.