Question
Draw ∠ABC = 120°. Bisect the angle using ruler and compasses only. Measure each 1 angle so obtained and check whether the angles obtained on bisecting ∠ABC are equal or not.
✓
Answer
Steps of Construction:
(i) Draw a line segment $BC$.
(ii) With centre $B$ and some suitable radius, draw an arc meeting $B C$ at $P$.
(iii) With centre $P$ and with the same radius, cut arcs $P Q$ and $Q R$.
(iv) Join $B R$ and produce it to $A$.
Then $\angle A B C=120^{\circ}$
(v) With centres $P$ and $R$, draw two arcs intersecting each other at $S$.
(vi) Join $B S$ and produce it to $D$. $B D$ is the bisector of $\angle A B C$.
On measuring each angle, it is of $60^{\circ}$ each. Yes, both angles are equal in measure.
(i) Draw a line segment $BC$.
(ii) With centre $B$ and some suitable radius, draw an arc meeting $B C$ at $P$.
(iii) With centre $P$ and with the same radius, cut arcs $P Q$ and $Q R$.
(iv) Join $B R$ and produce it to $A$.
Then $\angle A B C=120^{\circ}$
(v) With centres $P$ and $R$, draw two arcs intersecting each other at $S$.
(vi) Join $B S$ and produce it to $D$. $B D$ is the bisector of $\angle A B C$.
On measuring each angle, it is of $60^{\circ}$ each. Yes, both angles are equal in measure.
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