Geometry - Angle Chasing 4

Geometry Level 2

Circle β \beta has its center at O O . Given that ∠ Q O P = 7 0 ∘ \angle QOP=70^\circ , find ∠ M Q S \angle MQS .

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4 5 ∘ 45^\circ 7 5 ∘ 75^\circ 6 5 ∘ 65^\circ 3 5 ∘ 35^\circ 5 5 ∘ 55^\circ

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1 solution

From the inscribed angle theorem, we have

∠ P S Q = 1 2 ( 70 ) = 35 \angle PSQ=\dfrac{1}{2}(70)=35

Thus,

∠ M Q S = 90 − 35 = \angle MQS=90-35= 5 5 ∘ 55^\circ

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