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In the diagram, TS is a tangent to the circle at S. |PR| and...

In the diagram, TS is a tangent to the circle at S. |PR| and < PQR = 177o. Calculate < PST.

In the diagram, TS is a tangent to the circle at S. |PR| and < PQR = 177^o. Calculate < PST.

A.

54^o

B.

44^o

C.

34^o

D.

27^o

View answer & explanation

Correct answer is A

In the diagram above, x₁ = 180^o - 117^o = 63^o(opposite angles of a cyclic quad.)

x₁ = x₂ (base angles of isos. $\Delta$ )

x₁ + x₂ + $\alpha$ = 180^o (sum of angles of a $\Delta$

63^o + 63^o + $\alpha$ = 180^o

$\alpha$ = 180^o - (63 + 63)^o

= 54^o

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