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°.