Consider the figure attached.
Let m(R)=α degrees and m(T)=β degrees.
1.
Angle R, is an inscribed angle, intercepting the arc WTS.
This means that the measure of the arc WTS is double the measure of the angle R,
so m(arc WTS) = 2α degrees.
2.
Similarly,
Angle T, is an inscribed angle, intercepting the arc WRS. So
m(arc WRS) = 2β degrees.
3.
m(arc WTS)+m(arc WRS)=360° since these arcs cover the whole circle.
thus
2α+2β=360°
divide by 2:
α+β=180°
this means T and R are supplementary angles.
Let m(R)=α degrees and m(T)=β degrees.
1.
Angle R, is an inscribed angle, intercepting the arc WTS.
This means that the measure of the arc WTS is double the measure of the angle R,
so m(arc WTS) = 2α degrees.
2.
Similarly,
Angle T, is an inscribed angle, intercepting the arc WRS. So
m(arc WRS) = 2β degrees.
3.
m(arc WTS)+m(arc WRS)=360° since these arcs cover the whole circle.
thus
2α+2β=360°
divide by 2:
α+β=180°
this means T and R are supplementary angles.