Question

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

Explanation:

Step1: Find the supplementary angle of $131^{\circ}$

When two parallel lines are cut by a transversal, the angle adjacent to $131^{\circ}$ (let's call it $\angle b$) and $131^{\circ}$ form a linear - pair. So, $\angle b+131^{\circ}=180^{\circ}$. Then $\angle b = 180^{\circ}-131^{\circ}=49^{\circ}$.

Step2: Use the property of parallel lines (corresponding angles or alternate - interior angles)

Since lines $M$ and $N$ are parallel, $\angle a$ and $\angle b$ are corresponding angles (or alternate - interior angles depending on the transversal's orientation). Corresponding angles (or alternate - interior angles) formed by a transversal intersecting two parallel lines are equal. So, $m\angle a=\angle b = 49^{\circ}$.

Answer:

$49$