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

One of the angle of a quadrilateral is of 108^{\circ} and the remaining three angles are equal. Find each of the three equal angles.

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Answer: 84^{\circ}

Solution.
Given that:
One of the angle of a quadrilateral is of 108^{\circ} and the remaining three angles are equal.
Let each of the three equal angles be x ^{\circ}

As we know that the sum of angles of a quadrilateral is 360 ^{\circ}
108^{\circ} + x^{\circ} + x^{\circ} + x^{\circ} = 360^{\circ}
3x^{\circ} + 108^{\circ}= 360^{\circ}
3x^{\circ} = 360^{\circ} – 108^{\circ}
3x^{\circ}= 252^{\circ}
x=\frac{252^{\circ}}{3}
x=84^{\circ}
Hence, each of the three equal angles is 84^{\circ}.

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