Question

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

Explanation:

Step1: Use the property of cyclic quadrilaterals

In a cyclic quadrilateral, the sum of opposite angles is \(180^{\circ}\). So, \(\angle K+\angle M = 180^{\circ}\) and \(\angle L+\angle N=180^{\circ}\).

Step2: Calculate \(\angle M\)

Given \(\angle K = 67^{\circ}\), then \(\angle M=180^{\circ}-\angle K\). Substitute \(\angle K = 67^{\circ}\) into the formula: \(\angle M = 180^{\circ}- 67^{\circ}=113^{\circ}\).

Step3: Calculate \(\angle N\)

Given \(\angle L = 119^{\circ}\), then \(\angle N=180^{\circ}-\angle L\). Substitute \(\angle L = 119^{\circ}\) into the formula: \(\angle N=180^{\circ}-119^{\circ} = 61^{\circ}\).

Answer:

\(m\angle M = 113^{\circ}\) and \(m\angle N = 61^{\circ}\) (the first option)