Question
Using ruler and compasses, construct the following angle:
67.5°
67.5°
✓
Answer
Steps of Construction:
(i) Draw a line segment $BC$.
(ii) With centre $B$ and some suitable radius, draw an arc meeting $B C$ at $P$.
(iii) With centre $P$ and with the same radius, cut $\operatorname{arcs} P Q$ and then $Q R$.
(iv) Bisect arc QR at $K$ and again bisect arc $Q K$ at $S$.
(v) Bisect again arc SQ at T.
(vi) Join $B T$ and produce it to $A$.
Then $\angle ABC =67 \frac{1}{2}^{\circ}$ or $67.5^{\circ}$
(i) Draw a line segment $BC$.
(ii) With centre $B$ and some suitable radius, draw an arc meeting $B C$ at $P$.
(iii) With centre $P$ and with the same radius, cut $\operatorname{arcs} P Q$ and then $Q R$.
(iv) Bisect arc QR at $K$ and again bisect arc $Q K$ at $S$.
(v) Bisect again arc SQ at T.
(vi) Join $B T$ and produce it to $A$.
Then $\angle ABC =67 \frac{1}{2}^{\circ}$ or $67.5^{\circ}$
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