In Fig. sides $P Q$ and $R Q$ of $Δ P Q R$ are produced to points $S$ and $T$ respectively. If $∠ S P R = 135^{\circ} a$ and $∠ P Q T = 110^{\circ}$ . Find $∠ P R Q$ .

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Solution

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.

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