Consider angle w an angle supplementary to one of the angle measures of the quadrilateral.
Also, consider angle z an angle supplementary to one of the angle measures of the quadrilateral.
1. w = 95, so its supplementary angle must be 105. We know that 105 is one of the measures of an interior angle in the quadrilateral. We still cannot calculate x + y. INSUFFICIENT.
2. z = 125, so so its supplementary angle must be 55. We know that 55 is one of the measures of an interior angle in the quadrilateral. We still cannot calculate x + y. INSUFFICIENT.
Together, we know that 105 and 55 are two of the interior angle measures of the quadrilateral. We know that, by definition, all quadrilaterals' interior angles total 360 degrees.
105 + 55 = 160. So we know that the other two interior angles of the quadrilateral total 360 - 160 = 200 degrees. Even though this total does not directly correspond to the sum of x and y, which are not interior angles of the quadrilateral, they are supplementary angles.
Imagine if the interior angle supplementary to x was 115. x would be 65.
Then imagine that the angle supplementary to y was 85. y would be 95.
It doesn't matter if we know what the missing interior angles are by themselves. We know they total 200 degrees, so x and y total 160 degrees.
Answer is C.
