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A quadrilateral PQRS is inscribed in a circle, A quadrilateral PQRS is inscribed in a circle. The measure of angle PQR is 85 degrees. What is the measure of arc PQR?

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Answer:

Measure of arc PQR is 190°

Step-by-step explanation:

First have a sketch of the quadrilateral PQRS inside a circle

You should notice that the intercepted angle is ∠PSR

You should remember that the intercepted arc PQR is twice the intercepted angle ∠PSR

Find the intercepted angle ∠PSR

Remember that in a quadrilateral opposite angles add up to 180°

Hence;

∠PQR+∠PSR=180°

85 + ∠PSR=180°

∠PSR=180°-85°=95°

Find arc PQR

Arc PQR =2×∠PSR

Arc PQR=2×95°

=190°

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