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

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Given that ∠SPR = 135° and ∠PQT =110°

From the figure 

∠SPR + ∠RPQ = 180° 

∠PQT + ∠PQR = 180° 

[∵ linear pair of angles] 

⇒ ∠RPQ = 180° – ∠SPR = 180° – 135° = 45° 

⇒ ∠PQR = 180° – ∠PQT = 180°-110° = 70° 

Now in APQR 

∠RPQ + ∠PQR + ∠PRQ = 180° 

[∵ angle sum property] 

∴ 45° + ’70° + ∠PRQ = 180° 

∴ ∠PRQ = 180°-115° = 65°

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