Question

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

Answer 1

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.