Question

With the help of a ruler and compasses it is not possible to construct an angle of
(a) $37\frac{1°}{2}$

(b) 40°

(c) $22\frac{1°}{2}$

(d) $67\frac{1°}{2}$

Answer 1

(a) Using a ruler and compass, construct an angle of 150°.
Bisect the angle to get an angle of 75°.
Again bisect the angle to get an angle of 37.5°.

(b) It is not possible to construct an angle of 40° with the help of a ruler and compass.

(c) Using a ruler and compass, construct an angle of 90°.
Bisect the angle to get an angle of 45°.
Again bisect the angle to get an angle of 22.5°.

(d) Using a ruler and compass, construct an angle of 270°.
Bisect the angle to get an angle of 135°.
Again bisect the angle to get an angle of 67.5°.
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Hence, the correct option is (b).