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In the diagram, \(P\hat{Q}S = 65^o, R\hat{P}S = 40^o\hspa...

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

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

A.

85^o

B.

60^o

C.

55^o

D.

45^o

View answer & explanation

Correct answer is C

< 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°

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