Question
Draw an obtuse angle. Bisect it. Measure each of the angles so obtained.
✓
Answer
Obtuse angles are those angles which are greater than $90^\circ $ but less than $180^\circ .$
Draw an obtuse angle $\angle\text{BAC}.$
With an appropriate radius and centre at $A,$ draw an arc such that it intersects $AB$ and $AC$ at $P$ and Q, respectively.
With centre $P$ and radius more than half of $PQ,$ draw an $ARC.$
With the same radius and centre at $Q,$ draw another arc intersecting the previous arc at $R.$
Join $A$ and $R$ and extend it to $X.$
The ray $AX$ is the required bisector of $\angle\text{BAC}.$
If we measure $\angle\text{BAR}$ and $\angle\text{CAR},$
we have $\angle\text{BAR}=\angle\text{CAR}=65^{\circ}$
Draw an obtuse angle $\angle\text{BAC}.$
With an appropriate radius and centre at $A,$ draw an arc such that it intersects $AB$ and $AC$ at $P$ and Q, respectively.
With centre $P$ and radius more than half of $PQ,$ draw an $ARC.$
With the same radius and centre at $Q,$ draw another arc intersecting the previous arc at $R.$
Join $A$ and $R$ and extend it to $X.$
The ray $AX$ is the required bisector of $\angle\text{BAC}.$
If we measure $\angle\text{BAR}$ and $\angle\text{CAR},$
we have $\angle\text{BAR}=\angle\text{CAR}=65^{\circ}$
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