Question

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

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

Solution

## The correct option is D $$84^o$$We know, by angle sum property, the sum of angles of a quadrilateral is $$360^o$$. Given, one angle is $$108^o$$ and remaining three angles are equal.Let the remaining angles be $$x^o,y^o,z^o$$.Since they are equal, $$x^o+y^o+z^o=$$ $$x^o+x^o+x^o=3x^o$$.Then, $$108^o+x^o+y^o+z^o=360^o$$$$\Rightarrow$$ $$108^o+3x^o=360^o$$ $$\Rightarrow$$ $$360^o - 108^o =3x^{\circ}$$$$\Rightarrow$$ $$252^o =3x^{\circ}$$ $$\Rightarrow$$ $$x^o=\dfrac{252^o}{3} =84^{\circ}$$. Therefore, each of the three remaining angle is $$x^o=84^o$$. Hence, option $$C$$ is correct.Mathematics

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