Question

Which equation could be used to solve for the measure of angle Q? Circle N is shown with a quadrilateral OPQR inscribed inside it. Angle O is labeled x degrees. Angle P is labeled y degrees. Angle Q is labeled z degrees. Angle R is labeled w degrees
z − (w + x) = 360
z + w + x = 360
z + x = 180
z + w = 180

Answer 1

(angle ROP) + (angle RQP) = 180° because supplementary angles are 180,

The answer is C. x+z=180

Answer 2

the picture in the attached figure

we know that
In any quadrilateral where the vertices are on the circumference of a circle, the opposite angles add up to $180$ degrees. 

So,
 in this problem
$angle x + angle z = 180$

therefore

the answer is
$x+z=180$