Question

Quadrilateral STRW is inscribed inside a circle as shown below. Write a proof showing that angles T and R are supplementary.

Answer 1

Minor point: the quadrilateral is STWR, not STRW. Vertices are named in order.

The measure of angle T is half the measure of arc WRS. The measure of angle R is half the measure of arc STW. The sum of the measures of the two arcs is the measure of a circle, 360°, so you have

... T + R = (WRS)/2 + (STW)/2

... ... = (WRS + STW)/2

... ... = 360°/2 = 180°

Since the sum of T and R is 180°, they are supplementary.