Question

In the figure, sides QP and RQ of ∆ PQR are produced to points * and T respectively. If ∠SPR = 135° and ∠PQT = 110°, find ∠PRQ

Answer 1

In the given figure, ∠SPR = 135° and

∠PQT = 110°. ∠PQT + ∠PQR = 180° [Linear pair axiom]

⇒ 110° + ∠PQR = 180°

⇒ ∠PQR = 180° – 110° = 70°

Also, ∠SPR + ∠QPR = 180° [Linear pair axiom]

⇒ 135° + ∠QPR = 180°

⇒ ∠QPS = 180° – 135° = 45°

Now, in the triangle PQR

∠PQR + ∠PRQ + ∠QPR = 180°

[Angle sum property of a triangle]

⇒ 70° + ∠PRQ + 45° = 180°

⇒ ∠PRQ + 115° = 180°

⇒ ∠PRQ = 180° – 115° = 65°

Hence, ∠ PRQ = 65° Ans.