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:

1. Recall properties of rectangles: All angles in a rectangle are right angles (90°). So, in rectangle QRST, ∠Q and ∠S are 90°, and sides QR || ST, QT || RS.
2. Analyze triangle QRT: In triangle QRT, ∠Q is 90°, so the sum of ∠QRT and ∠QTR must be 180° - 90° = 90° (since the sum of angles in a triangle is 180°).
3. Define complementary angles: Two angles are complementary if their sum is 90°. Since ∠QRT + ∠QTR = 90°, they are complementary.
4. Eliminate other options:

• They are not congruent (unless the rectangle is a square, but no info given).
• Supplementary angles sum to 180°, which they don't.
• They are not right angles (right angles are 90°, their sum is 90°, so each is less than 90°).

Answer:

They are complementary.