Answer:
∠ QPR = 56°
Step-by-step explanation:
Δ RST is isosceles ( 2 congruent sides ) , then base angles are congruent
∠ SRT = [tex]\frac{180-44}{2}[/tex] = [tex]\frac{136}{2}[/tex] = 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 = [tex]\frac{180-68}{2}[/tex] = [tex]\frac{112}{2}[/tex] = 56°
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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
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
