In the diagram PST is a straight line PQ QS RS ... - JAMB Mathematics 2002 Question

In the diagram, PST is a straight line, PQ = QS = RS. If < RST = 72^o, find x

< QPS = < QSP = QRS = X

since PQ = QS = RS

< RQS = 2x - exterior angle

< RSQ = 180 - x

2x + x(188 - x) = 180

3x + 108 - x = 180 - x

2x + 108 = 180

2x = 180 - 108 = 72

x = (\frac{72}{2})

= 36^o