In the diagram, (Phat{Q}S = 65^o, Rhat{P}S = 40^2hspace{1mm}andhspace{1mm}Qhat{S}R=20^ohspace{1mm}Phat{S}Q)
-
A.
85o -
B.
60o -
C.
55o -
D.
45o
Correct Answer: Option C
Explanation
< 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°