Question

explore the properties of inscribed angles by following these steps. angle measures change. when ac changes, m∠abc and m∠adc change and are always equal to each other. 2. move points d and b and observe how the angle measures change. what happens to the angle measures? they change. they do not change. check

Explanation:

Step1: Recall inscribed - angle property

Inscribed angles subtended by the same arc are equal. When the arc (in this case $\overset{\frown}{AC}$) changes, the inscribed - angles ($\angle ABC$ and $\angle ADC$) subtended by it change. Also, as long as they are subtended by the same arc, they remain equal.

Step2: Analyze point - movement effect

When points $D$ and $B$ are moved, the arcs subtended by the angles change, so the angle measures change.

Answer:

They change.