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

Arc WTS is twice the measurement of angle R.
So arc WTS equals 2R
Arc WRS is twice the measurement of Angle T.
So arc WRS equals 2T
The sum of the two arcs WTS and WRS equal 360 degrees,
So now we have 2R + 2T = 360.
Divide all terms by 2:
R + T = 180
The sum of supplementary angles equal 180 degrees, therefore angles T and R are supplementary.