Question

explore the properties of inscribed angles by following these steps.

1. make a conjecture. which measures will change if you move vertex b of the inscribed angle? angle abc
2. move vertex b and observe what happens to the angle measures. was your conjecture correct? yes no

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle $\angle ABC$ is half of the measure of the intercepted arc $\overset{\frown}{AC}$, i.e., $m\angle ABC=\frac{1}{2}m\overset{\frown}{AC}$.

Step2: Analyze effect of moving vertex B

When vertex B of the inscribed angle $\angle ABC$ is moved along the circle (while A and C remain fixed), the measure of the intercepted arc $\overset{\frown}{AC}$ remains the same if A and C are fixed - endpoints. However, the measure of the inscribed angle $\angle ABC$ will change. This is because the relationship between the inscribed - angle and the intercepted arc is based on the position of the vertex on the circle.

Answer:

The measure of angle ABC will change if you move vertex B of the inscribed angle. When you move vertex B and observe, you will find that the conjecture is correct. So the answer for the second - part is yes.