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Question

One angle of a quadrilateral is of 108o and the remaining three angles are equal. Find each of the three equal angles.

A
64o
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B
74o
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C
84o
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D
94o
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Solution

The correct option is D 84o

We know, by angle sum property, the sum of angles of a quadrilateral is 360o.

Given, one angle is 108o and remaining three angles are equal.

Let the remaining angles be xo,yo,zo.

Since they are equal, xo+yo+zo= xo+xo+xo=3xo.

Then, 108o+xo+yo+zo=360o

108o+3xo=360o

360o108o=3x

252o=3x

xo=252o3=84.

Therefore, each of the three remaining angle is xo=84o.

Hence, option C is correct.


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