Question

Sides QP and RQ of ΔPQR are produced to points S and T respectively. If ∠SPR =135° and ∠PQT = 110° find ∠PRQ. In Fig. 6.39.

Answer 1

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◾◾here is your answer...

Solution:

∠SPR+∠QPR=180°    (Linear Pair)

⇒∠QPR=180°−∠SPR=180°−135°=45°

∠PQT=∠QPR+∠PRQ

 (If a side of a triangle is produced, then the exterior angle is equal to the sum of two interior opposite angles.)

⇒110°=45°+∠PRQ

⇒∠PRQ=110°−45°=65°

I hope, this will help you.

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Answer 2

110° - 180° = X (linear pair)

70° = X

Now, 180° - 135° = y (linear pair)

45° = y

Then

X + Y + Z = 180 (angle sum property)

70° + 45° - Z = 180

115 + Z = 180

Z = 180 - 115

Z = 65°