Question

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?

Answer 1

Measure of arc PQR is 190°

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°