WAEC - Mathematics (2003 - No. 26)

In the diagram, \(P\hat{Q}S = 65^o, R\hat{P}S = 40^o\hspace{1mm}and\hspace{1mm}Q\hat{S}R=20^o\hspace{1mm} Find P\hat{S}Q\)

85^o

60^o

55^o

45^o

< QPS = < PRS = 65° (angles in the same segment)

< PSR + 40° + 65° = 180°

< PSR + 105° = 180°

< PSR = 75°

< PSR = < PSQ + < QSR

75° = < PSQ + 20° \(\implies\) < PSQ = 75° - 20° = 55°