Question

which relationship must be true?
a ac = ab
b m∠b = 90°
c ab + bc = ac
d m∠a + m∠b + m∠c = 360°

1. quadrilateral qrst is inscribed in circle f, as shown.

the measure of ∠qts is 87°.
what is m∠qrs?

Explanation:

Step1: Recall property of cyclic quadrilateral

In a cyclic quadrilateral, opposite angles are supplementary. That is, the sum of the measures of opposite angles is 180°.

Step2: Identify opposite angles

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

Step3: Calculate m∠QRS

Let m∠QRS = x. Since ∠QTS and ∠QRS are supplementary and m∠QTS = 87°, we have the equation x+87° = 180°. Solving for x: x=180° - 87° = 93°.

Answer:

93°