Question
Use a pair of compasses and construct the following angles: $45^\circ $
✓
Answer
Steps of Construction:
1. Draw a ray $OA.$
2. With $O$ as centre and any su itable radius draw an arc above $O A$ to cut it at $B$.
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 $O E$. Then $\angle A O E=90^{\circ}$.
7. Draw the bisector OF of angle $\angle AOE$.
Then, $\angle\text{AOF}=45^\circ$ is the required angle.
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