Question

In a cyclic quadrilateral ABCD , AB || CD and ∠ B = 65 ° , find the remaining angles

Answer 1

PQ is a diameter of the circle 

∴ CPRQ = 90°  (angle is a semi cirde) 

∠ RPQ = 40°   (given) 

In Δ PQR, 

∠ PRQ + ∠ RQP + ∠ QPR = 180  (Angle sum property)

90 + ∠ RQP + 40 = 180

∠ RQP  = 50 °