Question

Two angles of a quadrilateral measure ${85}^0$ and ${75}^0$ respectively. The other two angles are equal. Find the measure of each of these equal angles.

• A. ${50}^{\circ }$
• B. ${100}^{\circ }$
• C. ${150}^{\circ }$
• D. ${200}^{\circ }$

Answer 1

The correct option is B ${100}^{\circ }$

Sum of 4 angles of a quadrilateral = ${360}^0$
Measures of two angles are ${85}^0,{75}^0$
The other two angles are equal. Let them be $x$.
So, ${85}^0+{75}^0+x+x={360}^{\circ }{160}^{\circ }+2x={360}^{\circ }2x={360}^{\circ }-{160}^{\circ }={200}^{\circ }2x={200}^{\circ }x=\frac{{200}^{\circ }}{2}={100}^{\circ }$
Thus, the measure of equal angles is ${100}^{\circ }.$