Question

Angle RSU is complementary to angle UST. Angle QSR is congruent to angle RSU.

Lines Q, R, U, and T extend from point S from left to right. Angle R S T is a right angle.
Which statement is true about angles UST and QSR?

They are complementary.
They are supplementary.
They are congruent.
They are obtuse.

Answer 1

They are complementary.

Reason: Let measure(RSU) = m. Then measure(QSR) = m (congruent) and measure(UST) = 90° − m (since RSU and UST are complementary). So measure(QSR) + measure(UST) = m + (90° − m) = 90°, hence the two angles are complementary.