Sum

In the following figure, m(arc PMQ) = 130^{o}, find ∠PQS.

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#### Solution

**Given :** m(arc PMQ) = 130°

**According to Tangent Chord Theorem,**The tangent chord angle theorem states that the measure of the angle formed by the intersection of a tangent and a chord of the circle equals one half of the intercepted arc by the chord.

∴ ∠PQS = `1/2` m(arc PMQ)

⇒ ∠PQS = `[130°]/2` = 65°

Concept: Angle Subtended by the Arc to the Point on the Circle

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