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Solve for the marked angle. ​

Solve for the marked angle. ​-example-1
User Raul Hugo
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1 Answer

4 votes

Answer:

m∠KQR = 69°

Explanation:

By the definition of intercepted arc and inscribed angle,

Intercepted arc measures the double of the inscribed angle.

m(arc KS + arc SR) = 2m∠KSR

132° + 90° = 2m∠KSR

m∠KSR = 111°

Since, quadrilateral KQRS is a cyclic quadrilateral,

m∠KSR + m∠KQR = 180°

111° + m∠KQR = 180°

m∠KQR = 180° - 111°

m∠KQR = 69°

m∠KQR = m∠Q = 69°

User Deterb
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