With the help of a ruler and a compass,it is | vedclass

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Question

(A) To construct an angle using a ruler and a compass,the angle must be a multiple of $7.5^{\circ}$ (which is half of $15^{\circ}$,which in turn is ha

Vedclass · Accepted Answer

$37.5$

Vedclass · Answer

(A) To construct an angle using a ruler and a compass,the angle must be a multiple of $7.5^{\circ}$ (which is half of $15^{\circ}$,which in turn is half of $30^{\circ}$,which is half of $60^{\circ}$). We can check the given options: $A) 37.5^{\circ} = 7.5^{\circ} 	imes 5$. Since $37.5^{\circ}$ is a multiple of $7.5^{\circ}$,it can be constructed by bisecting $75^{\circ}$ (which is $60^{\circ} + 15^{\circ}$). $B) 35^{\circ}$ is not a multiple of $7.5^{\circ}$. $C) 40^{\circ}$ is not a multiple of $7.5^{\circ}$. $D) 47.5^{\circ}$ is not a multiple of $7.5^{\circ}$. Thus,$37.5^{\circ}$ is the only angle among the options that can be constructed.

With the help of a ruler and a compass,it is possible to construct an angle of: (in $^{\circ}$)

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Write True or False and give reasons for your answer.
An angle of $67.5^{\circ}$ can be constructed.

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