Question

Two angles of a quadrilateral measure ${85}^{\circ }$ and ${75}^{\circ }$ respectively. The other two angles are equal.

Find the measure of each of these equal angles.

• A. ${240}^{\circ }$
• B. ${100}^{\circ }$
• C. ${80}^{\circ }$
• D. ${135}^{\circ }$

Answer 1

The correct option is B

${100}^{\circ }$

Let the measure of other equal angles be $x^{\circ }$.

The sum of all the angles of a quadrilateral is ${360}^{\circ }$.

$x^{\circ }+x^{\circ }+{85}^{\circ }+{75}^{\circ }={360}^{\circ }$

$\Rightarrow {160}^{\circ }+2x={360}^{\circ }$

$\Rightarrow 2x={360}^{\circ }–{160}^{\circ }$

$\Rightarrow 2x={200}^{\circ }$

$\Rightarrow x={100}^{\circ }$

Thus, the measure of other two equal angles is ${100}^{\circ }$.