Question

In the figure below, triangle QRS is isosceles, with QR SR.

If mSPQ = 36° and mQRS = 32°, what is mPQR?
A.
118°
B.
138°
C.
133°
D.
128°

Answer 1

D

Explanation:

since Δ QRS is isosceles then the base angles are congruent , that is

∠ RQS = ∠ RSQ = (180 - ∠ QRS ) ÷ 2 = (180 - 32)° ÷ 2 = 148° ÷ 2 = 74°

the sum of the 3 angles in Δ SPQ = 180° , then

∠ PQS = 180° - ∠ SPQ - ∠ PSQ = 180° - 36° - 90° = 54°

Then

∠ PQR = ∠ RQS + ∠ PQS = 74° + 54° = 128°

Answer 2

All angles in triangle QRS are equal since it is isosceles, so If mQRS = 32, subtract that from 180. 180-32=148°.
Now divided 148/2 to get 74°.
In triangle SPQ, there is one right angle 90°, and mSPQ 36°
Add 90+36=126 and subtract that from 180 again
180-126=54°
Add 74° and 54° = 128°

The answer is D