Question

Draw $\angle ABC={120}^{\circ }.$ Bisect the angle using the ruler and compasses only. Measure each angle so obtained and check whether the angles obtained on bisecting $\angle ABC$ are equal or not.

Answer 1

Steps of Construction:
1.Construct a line segment $BC$.
2.Taking $B$ as centre and some suitable radius construct an arc which meets $BC$ at the point $P$.
3. Taking $P$ as centre and with same radius cut off the arcs $PQ$ and $QR$.
4.Now join $BR$ and produce it to point $A$
$\angle ABC={120}^o$
5.Taking $P$ and $R$ as centres construct two arcs which intersect each other at the points $S$.
6.Now join $BS$ and produce it to point $D$.
Here $BD$ is the bisector of $\angle ABC$
By measuring each angle we get to know that is it ${60}^o$ yes,both the angles are of equal measure.