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Question
With the help of a ruler and a compass it is not possible to construct an angle of ______.
Options
37.5°
40°
22.5°
67.5°
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Solution
With the help of a ruler and a compass it is not possible to construct an angle of 40°.
Explanation:
Considering option (A):
`37.5^circ = 1/2 xx 75^circ`
75° can be constructed with the help of a ruler and a compass.
Considering option (B):
`40^circ = 1/2 xx 20^circ`
This is not possible.
20° cannot be constructed with the help of a ruler and a compass.
Considering option (C):
`22.5^circ = 1/2 xx 45^circ`
45° can be constructed with the help of a ruler and a compass.
Considering option (D):
`67.5^circ = 1/2 xx 135^circ`
= `1/2 xx (90^circ + 45^circ)`
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 ruler and compass is the correct answer.
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