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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
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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 $$84^o$$

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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