Question

angle rsu is complementary to angle ust. angle qsr is congruent to angle rsu. which statement is true about angles ust and qsr? they are complementary. they are supplementary. they are congruent. they are obtuse.

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles add up to \(90^{\circ}\). Given \(\angle RSU+\angle UST = 90^{\circ}\)

Step2: Use the congruent - angle property

Since \(\angle QSR\cong\angle RSU\), then \(\angle QSR=\angle RSU\) (by the definition of congruent angles: congruent angles have equal measures)

Step3: Substitute \(\angle RSU\) with \(\angle QSR\)

Substitute \(\angle RSU\) in \(\angle RSU+\angle UST = 90^{\circ}\) with \(\angle QSR\). We get \(\angle QSR+\angle UST=90^{\circ}\)

Answer:

They are complementary.