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. ${64}^o$
• B. ${74}^o$
• C. ${84}^o$
• D. ${94}^o$

Answer 1

Answer: (C)

${84}^o$

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, ${108}^o+x^o+y^o+z^o={360}^o$

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

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

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

$\Rightarrow$ $x^o=\frac{{252}^o}{3}={84}^{\circ }$.

Therefore, each of the three remaining angle is $x^o={84}^o$.

Hence, option $C$ is correct.