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In the following figure, m(arc PMQ) = 130o, find ∠PQS. - Geometry

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Sum

In the following figure, m(arc PMQ) = 130o, 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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