In the diagram SR QR lt SRP 65o and lt RPQ 48o ... - WAEC Mathematics 2012 Question

< RSQ = < RPQ = 48^o (angle in the same segment)

< SQR < RSQ (Base angle of an isosceles \(\bigtriangleup\))

< SQR = 480

< QRS + < RSQ + < RSQ = 180^o(sum of interior angles of a \(\bigtriangleup\))

i.e. < QRS + 48^o + 48^o = 180

< QRS = 180 - (48 + 48) = 180 - 96 = 84^o

but < PRQ + < PRS = < QRS

< PRQ = < QRS - < PRS - 84 - 65

= 19^o