Question

Draw an angle of ${80}^{\circ }$ using a protractor and divide it into four equal parts, using ruler and compasses. Check your construction by measurement.

Answer 1

Steps of construction:

Step I- With the help of protractor, draw an angle of ${80}^{\circ }$. Name the rays $OA$ and $OB$.

Step II - Cut $OA$ and $OB$ at $Q$ and $P$, taking $O$ as the center and any convenient radius, with the help of the compass.

Step III - With vertex $P$, by using compass take more than half of arc $PQ$ and draw arc.

Step IV - With vertex $Q$, by using compass with same length, cut the previous arc at $R$.

Step V- With help of ruler, join the point $O$ and $R$.

$\therefore$ $\angle AOR=\angle ROB$

Step VI - Similarly, bisect the arcs $QS$ and $SP$

$\therefore$ $\angle AOV=\angle VOR$ and $\angle ROU=\angle UOB$

Thus, $\angle AOV$, $\angle VOR$, $\angle ROU$ and $\angle UOB$ divide $\angle BOA$ in four equal parts

You can verify this by using a protractor.

$\therefore \angle AOV=\angle VOR=\angle ROU=\angle UOB={20}^{\circ }$

Hence, required construction is formed.