Question

line ab is parallel to line cd. what is the measure of ∠4? 100° 180° 120° 10°

Explanation:

Step1: Identify corresponding angles

Since line AB is parallel to line CD, $\angle4$ and the $80^{\circ}$ angle are corresponding angles.

Step2: Apply corresponding - angles property

Corresponding angles of parallel lines are equal. So, $m\angle4 = 80^{\circ}$. But if we consider the linear - pair relationship with the adjacent angle to $\angle4$. The adjacent angle to $\angle4$ forms a linear pair with the $80^{\circ}$ corresponding angle. A linear pair of angles sums to $180^{\circ}$. Let the measure of $\angle4=x$. The angle adjacent to $\angle4$ and the $80^{\circ}$ angle are supplementary. Since $\angle4$ and the $80^{\circ}$ angle are corresponding angles, and we know that the angle adjacent to $\angle4$ and $\angle4$ sum to $180^{\circ}$, we can also note that the angle adjacent to the $80^{\circ}$ angle (let's call it $\alpha$) and $\angle4$ are vertical angles. Vertical angles are equal. The angle adjacent to the $80^{\circ}$ angle is $180 - 80=100^{\circ}$. And $\angle4$ and this adjacent angle are vertical angles. So, $m\angle4 = 100^{\circ}$.

Answer:

$100^{\circ}$