In the fiqure where PQRTU is a circle, ISTI = IRSI and angle TSR = 52o. Find the angle marked m

In the fiqure where PQRTU is a circle, ISTI = IRSI and angle TSR = 52o. Find the angle marked m

A.

128o

B.

52o

C.

104o

D.

64o

E.

116o

Correct answer is E

< STR = \(\frac{180 - 52}{2}\) = \(\frac{128}{2}\) = 64o

< PTR = 180 - < STR(angle on a straight line)

= 180 - 64 = 116o

< PQR + < PTR = 180(Supplementary)

< PQR + 118 = 180

< PQR = 180 - 118

= 64

M = 180 - < PQR

= 180 - < PQR = 180 - 64

= 116o