Question

part a
∠adb and ∠bdc represent a linear pair because points a, d, and c lie on a straight line. calculate the sum of m∠adb and m∠bdc. then, move point b around and see how the angles change. what happens to the sum of m∠adb and m∠bdc as you move point b around?

Explanation:

A linear pair of angles are adjacent angles formed by two intersecting lines that lie on a straight line, so their measures add up to the measure of a straight angle. A straight angle has a fixed measure of 180 degrees. Moving point B changes the individual measures of ∠ADB and ∠BDC, but they remain a linear pair as points A, D, C stay collinear.

Answer:

The sum of $m\angle ADB$ and $m\angle BDC$ is $180^\circ$. As point B is moved around, the sum of the measures of the two angles remains $180^\circ$ (constant) because they always form a linear pair on the straight line AC.