Elementary Geometry for College Students (6th Edition)

The inscribed angles R and T intercept two arcs whose sum makes up a whole circle, which is 360$^{\circ}$. Since the measure of an inscribed angle is equal to half the measure of its intercepted arc, the sum of R and T must be half the measure of the sum of their arcs, which is 360/2=180$^{\circ}$. When the sum of the measures of two angles is equal to 180, they are supplementary angles.