Question
Use a pair of compasses and construct the following angles: $22\frac{1}{2}^\circ$
✓
Answer
Steps of Construction:
$1.$Draw a ray $OA.$
$2.$With $O$ as centre and any suitable radius draw an arc above $OA,$ cutting 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 $CD$ 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 $\angle\text{AOE}.$
$8.$Draw the bisector $OG$ of $\angle\text{AOF}.$
Then, $\angle\text{AOG}=22\frac{1}{2}^\circ$ is the required angle.
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