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Question

(C) Angles that can be constructed using a ruler and a compass are those that are multiples of $3.75^{\circ}$ or can be derived by bisecting standard

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(C) Angles that can be constructed using a ruler and a compass are those that are multiples of $3.75^{\circ}$ or can be derived by bisecting standard angles like $60^{\circ}, 90^{\circ}, 45^{\circ}, 30^{\circ}$,etc.$37.5^{\circ}$ is half of $75^{\circ}$,which is constructible.$22.5^{\circ}$ is half of $45^{\circ}$,which is constructible.$67.5^{\circ}$ is half of $135^{\circ}$,which is constructible.However,$40^{\circ}$ cannot be constructed using only a ruler and a compass because it is not a multiple of $3.75^{\circ}$ and cannot be obtained by repeated bisection of standard constructible angles.

With the help of a ruler and a compass,it is not possible to construct an angle of: (in $^{\circ}$)

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