Question

lines m and n are parallel. find the measure of ∠a. m∠a = ?°

Explanation:

Step1: Find the supplementary angle of \(116^{\circ}\)

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. Let the angle adjacent to \(116^{\circ}\) be \(x\). Then \(x + 116^{\circ}=180^{\circ}\), so \(x = 180^{\circ}- 116^{\circ}=64^{\circ}\).

Step2: Use the property of alternate interior angles

Since lines \(M\) and \(N\) are parallel and cut by a transversal, \(\angle a\) and \(x\) are alternate interior angles. Alternate interior angles are equal. So \(\angle a=x\).

Answer:

\(64\)