Question

angle k measures 67° and angle l measures 119°. what are the measures of angles m and n? m∠m = 61° and m∠n = 113° m∠m = 67° and m∠n = 119° m∠m = 113° and m∠n = 61° m∠m = 119° and m∠n = 67°

Explanation:

Step1: Recall property of cyclic quadrilateral

In a cyclic quadrilateral, opposite angles are supplementary (sum to 180°).

Step2: Find measure of angle M

Since angle K and angle M are opposite angles in the cyclic - quadrilateral, and \(m\angle K = 67^{\circ}\), then \(m\angle M=180^{\circ}-m\angle K\). So \(m\angle M = 180 - 67=113^{\circ}\).

Step3: Find measure of angle N

Since angle L and angle N are opposite angles in the cyclic - quadrilateral, and \(m\angle L = 119^{\circ}\), then \(m\angle N=180^{\circ}-m\angle L\). So \(m\angle N = 180 - 119 = 61^{\circ}\).

Answer:

\(m\angle M = 113^{\circ}\) and \(m\angle N = 61^{\circ}\), which corresponds to the option: \(m\angle M = 113^{\circ}\) and \(m\angle N = 61^{\circ}\) (the third option in the multiple - choice list)