We are given two parallel lines intersected by a transversal. Angle A is given as $160^\circ$. We need to find the measure of angle B.

1. Problem Description

We are given two parallel lines intersected by a transversal. Angle A is given as $160^\circ$. We need to find the measure of angle B.

2. Solution Steps

Since the two lines are parallel, and they are intersected by a transversal, angle A and angle B are same-side interior angles (also known as consecutive interior angles).

Same-side interior angles are supplementary, which means their measures add up to $180^\circ$.

Therefore, we have:

$m\angle A + m\angle B = 180^\circ$.

We are given that $m\angle A = 160^\circ$. Substituting this into the equation, we get:

$160^\circ + m\angle B = 180^\circ$.

Subtracting $160^\circ$ from both sides, we find:

$m\angle B = 180^\circ - 160^\circ$.

$m\angle B = 20^\circ$.

3. Final Answer

The measure of angle B is $20^\circ$.