# Rectangle QRST is shown. Angle QRT is congruent to angle STR, and angle STR is complementary to angle QTR.Which statement is

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?

1).They are congruent.

2).They are complementary.

3).They are supplementary.

4).They are right angles.

## This Post Has 10 Comments

1. elizabethann2 says:

1)The sum of the angles A B C is 180 degrees (a line). Reason: All triangles have this property.
2) 2 right angles are supplementary (add up to a line). Reason: If we have a normal to a line, the two resulting angles are right and they add up to a line.
3) A is supplementary to the sum of B and C. Reason: 1)
4) A right angle is supplementary to A. Reason: 2)
5) The sum of B and C is a right angle. Hence, B and C are complimentary. Reason: This results from 3 and 4 and congruency of angles.

2. amortegaa805 says:

proved

Step-by-step explanation:

In Triangle ABC angle C is 90°

Also we know that ∠A+ ∠B+∠C= 180°1

now since ∠C= 90°

putting ∠C= 90° in 1  we get

⇒∠A+ ∠B= 180°-90°

⇒∠A+ ∠B= 90°

Since, sum of angle A and B is 90° therefore they are complementary to each other.

3. smithmalyk4 says:

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.

4. micahmckay05 says:

Therefore.

angle 1 is congruent to angle 3 ...Proved

The proof with steps are below with Fill in the blanks

Step-by-step explanation:

Complementary Angles:

Two angles are Complementary when they add up to 90 degrees.

Example 40° and 50° are Complementary Angles.

If 'x' and 'y' are Complementary Angles the we have

$x+y=90\°$

Here,

Given:

angle 1 and angle 2 are complementary

angle 3 and angle 2 are complementary

To Prove:

angle 1 is congruent to angle 3

Proof:

Step 1:

angle 1 and angle 2 are complementary and angle 3 and angle 2 are complementary because it is Given.

Step 2:

By the definition of complementary angles,

m of angle 1 + m of angle 2 = _90°__ and m of angle 3 + m of angle 2 = _90°_.

Step 3:

Transitive Property of Equality.

Then m of angle 1 + m of angle 2 = m of angle 3 + m of angle 2 by the Transitive Property of Equality.

Step 4:

Subtract m of angle 2 from each side. By the Subtraction Property of Equality, you get

$m\angle 1 +m\angle 2-m\angle 2=m\angle 3+m\angle 2-m\angle 2$

$m\angle 1=m\angle 3$

m of angle 1 = _measure of angle_3_.

Step 5:

Angles with the same measure are _Congruent__,

Step 6:

so angle 1 is congruent to angle 3.

Therefore.

angle 1 is congruent to angle 3 ...Proved

5. nev322 says:

They are complementary.

Step-by-step explanation:

I made a small visual (mainly so I could visualize it but I figured it might help you too).

Since QRT is congruent to STR, QTR and SRT are also congruent.

Therefore, since STR is complementary to QTR, and STR is congruent to QRT, QTR must be complementary to QRT due to the transitive property.

$Rectangle QRST is shown. Angle QRT is congruent to angle STR, and angle STR is complementary to angl$

6. acavalieri72 says:

They are complementary

Step-by-step explanation:

7. tdowling331 says:

The correct answer for #1 is a net i’m working on the 2nd

8. fvmousdiana says:

answer: i'm just going to u on one

explanation:   for the first answer is b. i got this because an orthographic drawing is a method that allows someone to represent a three-dimensional object on a two-dimensional piece of paper.

9. angel0203wilcox says:

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.

10. loki285 says:

The angle that is complementary to the angle of 22 degrees is the angle of 68 degrees. This is because when you add the two values, their sum equals 90 degrees.