Question
Use a pair of compasses and construct the following angles:
$67\frac{1}{2}^\circ$
$67\frac{1}{2}^\circ$
✓
Answer
Steps of Construction:
1. Draw a ray $OA.$
2. With $O$ as centre and any suitable radius draw an arc above $O A$ to cut it $B$.
3. With $B$ as centre and same radius cut the previous arc at $C$ and then with $C$ as centre and same radius cut the arc at $D$.
4. With $C$ as centre and radius more than half $C D$ draw an arc.
5. With $D$ as centre and same radius draw another arc to cut the previous arc at $E$.
6. Join $OE$ . Then $\angle AOE =90^{\circ}$.
7. Draw the bisector $OF$ of $\angle AOE$.
8. Draw the bisector $OG$ of $\angle EOF$.
Then, $\angle\text{AOG}=67\frac{1}{2}^\circ$ is the required angle.
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