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In Fig.  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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Arms of the ∆PQR QP and RP are produced to S and T and ∠PQT 

= 110°, ∠SPR = 135°. 

∠PRQ = ? 

Straight line PR is on straight line SQ. 

∠SPR and ∠RPQ are Adjacent angles. 

∴ ∠SPR + ∠RPQ = 180° 

135 + ∠RPQ = 180° 

∴ ∠RPQ =180 – 135 

∠RPQ = 45° 

(i) Similarly QP straight line is on straight line TR. 

∠TQP and ∠PQR are Adjacent angles. 

∴ ∠RQP + ∠PQR = 180° 

110 + ∠PQR = 180° 

∠PQR = 180 – 110 

∴ ∠PQR = 70° 

Now, in ∆PQR, 

∠QPR + ∠PQR + ∠PRQ = 180° 

45 + 70 + ∠PRQ = 180° 

115 + ∠PRQ = 180° 

∠PRQ = 180 – 115 

∴ ∠PRQ = 65°.

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