Question

lines m and n are parallel. find the measure of ∠a. m n 131° m∠a = ?°

Explanation:

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

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary.
Let the angle adjacent to $\angle a$ (on the same side of the transversal as the $131^{\circ}$ angle) be $x$. Then $x + 131^{\circ}=180^{\circ}$. So $x = 180^{\circ}-131^{\circ}=49^{\circ}$.

Step2: Use the property of vertical angles

$\angle a$ and $x$ are vertical angles. Vertical angles are equal. So $m\angle a=x = 49^{\circ}$.

Answer:

$49$