In the diagram, \(P\hat{Q}S = 65^o, R\hat{P}S = 40^o\hspace{1mm}and\hspace{1mm}Q\hat{S}R=20^o\hspace{1mm} Find P\hat{S}Q\)
Attached Figure / Diagram
A
85o
B
60o
C
55o
D
45o
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
< QPS = < PRS = 65^\circ (angles in the same segment)
< PSR + 40^\circ + 65^\circ = 180^\circ
< PSR + 105^\circ = 180^\circ
< PSR = 75^\circ
< PSR = < PSQ + < QSR
75^\circ = < PSQ + 20^\circ \(\implies\) < PSQ = 75^\circ - 20^\circ = 55^\circ
Source: Myschool Past Questions Archive (Record #26595)