Question
Using ruler and compasses, construct the following angle:
22.5°
22.5°
✓
Answer
Steps of Construction:
(i) Draw a line segment $B C$.
(ii) With centre B and some suitable radius, draw an arc meeting $B C$ at $P$.
(iii) With centre $P$ and some radius, cut off $\operatorname{arcs~} PQ$.
(iv) Bisect arc $P Q$ at $R$ and join $B R$.
(v) Bisect arc QR at $S$ and join BS.
(vi) Now bisect arc PR at T.
(vii) Join BT and produce it to A.
Then $\angle ABC =22 \frac{1}{2}^{\circ}$ or $22.5^{\circ}$.
(i) Draw a line segment $B C$.
(ii) With centre B and some suitable radius, draw an arc meeting $B C$ at $P$.
(iii) With centre $P$ and some radius, cut off $\operatorname{arcs~} PQ$.
(iv) Bisect arc $P Q$ at $R$ and join $B R$.
(v) Bisect arc QR at $S$ and join BS.
(vi) Now bisect arc PR at T.
(vii) Join BT and produce it to A.
Then $\angle ABC =22 \frac{1}{2}^{\circ}$ or $22.5^{\circ}$.
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