Question

1. quadrilateral qrst is inscribed in circle f, as shown. the measure of ∠qts is 87°. what is m∠qrs?

Explanation:

Step1: Recall the property of cyclic quadrilaterals

Opposite angles of a cyclic quadrilateral are supplementary, i.e., they add up to 180°.

Step2: Identify opposite angles

In cyclic quadrilateral QRST, ∠QTS and ∠QRS are opposite angles.

Step3: Calculate the measure of ∠QRS

Let \(m\angle QRS = x\). Since \(m\angle QTS + m\angle QRS=180^{\circ}\) and \(m\angle QTS = 87^{\circ}\), then \(x = 180 - 87\).
\(x=93^{\circ}\)

Answer:

\(93^{\circ}\)