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, ∠QRS, ∠RST, ∠STQ, and ∠TQR are 90°. Also, the diagonal RT divides the rectangle, and we use the given congruence and complementary relationships.
2. Given: ∠QRT ≅ ∠STR, and ∠STR is complementary to ∠QTR (i.e., ∠STR + ∠QTR = 90°).
3. Substitute ∠QRT for ∠STR (since they are congruent): ∠QRT + ∠QTR = 90°.
4. In triangle QRT, the sum of angles ∠QRT, ∠QTR, and ∠RQT (which is a right angle, 90°) should be 180°, but we focus on ∠QRT and ∠QTR. Since their sum is 90°, they are complementary.

Answer:

They are complementary.