Q1Written answer
With the help of a ruler and a compass, it is not possible to construct an angle of :
(A) 37.5°
(B) 40°
(C) 22.5°
(D) 67.5°
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Worked solution
(B) 40°
Explanation:
Considering Option (A):
37.5° = ½ × 75°
75° can be constructed with the help of a ruler and a compass.
Considering Option (B):
40° = ½ × 20°
This is not possible.
20° cannot be constructed with the help of a ruler and a compass.
Considering Option (C):
22.5° = ½ × 45°
45° can be constructed with the help of a ruler and a compass.
Considering Option (D):
67.5° = 1/2 × 135° = 1/2 × (90° + 45°)
Both 90° and 45° can be constructed with the help of a ruler and a compass.
Hence, option (B), is not possible to construct an angle of 40° with the help of a ruler and compass is the correct answer.