Question

rectangle qrst is shown. angle qrt is congruent to angle str, and angle str is complementary to angle qtr. which statement is true about angles qrt and qtr? they are congruent. they are complementary. they are supplementary. they are right angles.

Explanation:

Step1: Recall angle - relationship definitions

Congruent angles have equal measure. Complementary angles sum to 90°. Supplementary angles sum to 180°. Right - angles measure 90°.

Step2: Use given information

We know that in rectangle QRST, ∠QRT≅∠STR and ∠STR + ∠QTR=90° (since ∠QTS = 90° and ∠QTS=∠STR + ∠QTR).

Step3: Substitute ∠QRT for ∠STR

Since ∠QRT≅∠STR, we can substitute ∠QRT for ∠STR in the equation ∠STR + ∠QTR = 90°. So, ∠QRT+∠QTR = 90°.

Answer:

They are complementary.