Question

APQR and ARST are shown.
S
R.
P
440
T
What is mZQPR?
m/OPR

Answer 1

Answer: 56

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Step-by-step explanation:

Triangle TRS is isosceles due to the sides TR and TS being congruent.

Let x be the measure of angle R of triangle TRS. It's also the measure of angle S. The base angles of any isosceles triangle are the same.

Add up the three angles of triangle TRS. Set the sum equal to 180. Solve for x.

T+R+S = 180

44+x+x = 180

44+2x = 180

2x = 180-44

2x = 136

x = 136/2

x = 68

This means angle TRS is 68 degrees.

Subsequently, it also means angle QRP is 68 degrees as well. These two angles are congruent vertical angles.

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Now focus on triangle PQR. This triangle is also isosceles.

We have the following interior angles

• P = y
• Q = y
• R = 68 (found in the previous section earlier)

So,

P+Q+R = 180

y+y+68 = 180

2y+68 = 180

2y = 180-68

2y = 112

y = 112/2

y = 56 is the measure of angle QPR

Answer 2

∠ QPR = 56°

Step-by-step explanation:

Δ RST is isosceles ( 2 congruent sides ) , then base angles are congruent

∠ SRT =
`(180-44)/(2)` =
`(136)/(2)` = 68°

∠ PRQ and ∠ SRT are vertically opposite angles and are congruent , so

∠ PRQ = 68°

Δ PRQ is isosceles ( 2 congruent sides ), then base angles are congruent , so

∠ QPR =
`(180-68)/(2)` =
`(112)/(2)` = 56°