Question

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Answer 1

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angle NPR + angle RPM = 180°

[ '.' Linear pair ]

.°. 150° + angle RPM = 180°

.°. angle RPM = 180° - 150°

.°. angle RPM = 30°

angle RPQ = 30°

Now, angle MQR + angle RQN = 180°

['.' Linear pair ]

.°. 45° + angle RQN = 180°

.°. angle RQN = 180° - 45°

.°. angle RQN = 135 °

angle RQP= 135°

Now,in ∆PQR

angle RQP + angle RPQ + angle PRQ = 180°

135° + 30° + angle PRQ = 180°

165° + angle PRQ= 180°

angle PRQ = 180° - 165°

angle PRQ = 15°