Question

One angle of a quadrilateral is of ${108}^{\circ }$ and the remaining three angles are equal. Find each of the three equal angles. Thinking Process:
The sum of all the angles in a quadrilateral is ${360}^{\circ }$, use this result and simplify it.

• A. ${78}^{\circ }$
• B. ${104}^{\circ }$
• C. ${72}^{\circ }$
• D. ${84}^{\circ }$

Answer 1

The correct option is D

${84}^{\circ }$

Let each of three equal angles be $x^{\circ }$.

Now, sum of angles of a quadrilateral = ${360}^{\circ }$

$\Rightarrow {108}^{\circ }+x^{\circ }+x^{\circ }+x^{\circ }={360}^{\circ }\Rightarrow 3x^{\circ }={360}^{\circ }-{108}^{\circ }$

$\Rightarrow x^{\circ }=\frac{{252}^{\circ }}{3}$

$\therefore x^{\circ }={84}^{\circ }$

Hence, each of the three equal angles is ${84}^{\circ }$.