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In the diagram, PS and RS are tangents to the circle cent...

In the diagram, PS and RS are tangents to the circle centre O. ∠PSR = 70°, ∠POR = m, and ∠PSR =n. Find ( m + n ).

In the diagram, PS and RS are tangents to the circle centre O. ∠PSR = 70°, ∠POR = m, and ∠PSR =n. Find ( m + n ).

A.

110 $^o$

B.

135 $^o$

C.

165 $^o$

D.

225 $^o$

View answer & explanation

Correct answer is C

In the diagram,

Thus, m = 2 x 55 $^o$ (is a bisector of obtuse

m = 110 $^o$

n = $\frac{1}{2}$ x 110 $^o$ (angle at centre = 2 x angle at circum)

n = 55 $^o$

m + n = 110 + 55 = 165 $^o$

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