Answer:
D
Explanation:
it is a regular pentagon.
so, all side lengths are equal, and also all cross connections between corners are equal.
that makes TR parallel to PQ.
and that makes SPQ an isoceles triangle (both legs are equally long). and the smaller triangle S to x to the angle to the right of x is similar to SPQ, which means they have the same angles.
so, the triangle interior angle at P = the triangle interior angle Q = y.
and they must be the same as the bottom 2 interior angles of the small triangle.
x and the angle right to x are equal too, as they are the triangle exterior (supplementary) angles to the bottom 2 interior angles of the small triangle.
we know that the sum of all angles of the internal trapezoid (PQ to x and its right neighbor) is 360.
and based on the EqualLogic found above these angles are
2×x + 2×y = 360°
x + y = 180°