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  • With the help of a ruler and a compass it is not possible to construct an angle of:

With the help of a ruler and a compass, it is not possible to construct an angle of :

(A) 37.5^{\circ}                 (B) 40^{\circ}                 (C) 22.5^{\circ}                   (D) 67.5^{\circ}

Answers (1)

Answer - 40^{\circ}

As we know that with the help of a ruler and a compass we can construct angles which are bisectors of other angles.               

37.5^{\circ} is a bisector of 75^{\circ}.

37.5^{\circ} = \frac{1}{2}\times 75^{\circ}

40^{\circ} is a bisector of 80^{\circ}.

40^{\circ} = \frac{1}{2}\times 80^{\circ}

22.5^{\circ} is a bisector of 45^{\circ}

22.5^{\circ} = \frac{1}{2}\times 45^{\circ}

67.5^{\circ} is a bisector of 135^{\circ}

67.5 ^{\circ}=\frac{1}{2}\times 135^{\circ}

75^{\circ}, 45 ^{\circ}and 135^{\circ} can be constructed with the help of a ruler and a compass as they are all multiples of 15 ^{\circ}.

Hence we can’t construct 40^{\circ} by the use of a ruler and compass.

Therefore option (B) is correct.

Posted by

infoexpert21

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