Question

using the image below, find the m∠x° and m∠y°. select one: a. x° = 72°, y° = 108° b. x° = 88°, y° = 92° c. x° = 92°, y° = 72° d. x° = 72°, y° = 92°

Explanation:

Step1: Recall property of cyclic quadrilateral

Opposite angles of a cyclic quadrilateral are supplementary (sum to 180°).

Step2: Find \(x\)

For the pair of opposite angles \(x\) and \(108^{\circ}\), we have \(x + 108^{\circ}=180^{\circ}\), so \(x=180^{\circ}- 108^{\circ}=72^{\circ}\).

Step3: Find \(y\)

For the pair of opposite angles \(y\) and \(88^{\circ}\), we have \(y + 88^{\circ}=180^{\circ}\), so \(y=180^{\circ}-88^{\circ}=92^{\circ}\).

Answer:

D. \(x^{\circ}=72^{\circ},y^{\circ}=92^{\circ}\)