Question
Use a pair of compasses and construct the following angles:$135^\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 as before draw another arc to cut the previous arc at $C.$ With $C$ as centre and same radius draw the arc to cut it at $D.$ Again with $D$ as centre and same radius cut the arc at $E.$
$4.$Join $OD$ and produce it to $G.$ Then $\angle\text{AOG}=120^\circ.$
$5.$With $D$ as centre and radius more than half $DE$ draw an arc.
$6.$With $E$ as centre and same radius draw another arc to cut the previous arc at $F$ Join $OF.$
$7.$Draw the bisector $OH$ of $\angle\text{GOF}.$
Then, $\angle\text{AOH}=135^\circ$ is the required angle.
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