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.

Answer 1

They are complementary.because they are in both in the right triangle.And we know that the sum of all the angles in a triangle is 180 degrees.So one angle is 90 degree and the other two must be a sum up to 90 degrees and hence they are complementary.

Answer 2

Rectangle qrst is shown. angle qrt is congruent to angle str, and angle str is complementary to angle qtr.

Rectangle can be split into two triangles qtr and str.

We know every angle in a triangle is 90 degree.

In a triangle qtr,  ∠rqt is 90 degree. Also we know the sum of angles in a triangle is 180 degree.

So ∠rqt + ∠qtr + ∠qrt = 180 degree

90 + ∠qtr + ∠qrt = 180 (Subtract 90 on both sides)

∠qtr + ∠qrt = 90

Hence , ∠qtr and  ∠qrt are complementary angles.