Question

explore the properties of inscribed angles by following these steps.
angle measures change.
when \\(\overset{\frown}{ac}\\) changes,
\\(m\angle abc\\) and \\(m\angle adc\\)
change and are
always equal to each other.

1. 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
\\(m\overset{\frown}{ac} = 104^\circ\\)
\\(m\angle abc = 52^\circ\\)
\\(m\angle adc = 52^\circ\\)

Explanation:

Step1: Recall Inscribed Angle Theorem

The measure of an inscribed angle is half the measure of its intercepted arc. For \(\angle ABC\) and \(\angle ADC\), both intercept arc \(\overset{\frown}{AC}\). The measure of \(\overset{\frown}{AC}\) is \(104^\circ\), so the measure of each inscribed angle is \(\frac{1}{2} \times 104^\circ = 52^\circ\).

Step2: Analyze Effect of Moving D and B

When points D and B are moved (while still on the circle), the intercepted arc \(\overset{\frown}{AC}\) does not change. Since the measure of an inscribed angle depends only on the measure of its intercepted arc, the measures of \(\angle ABC\) and \(\angle ADC\) will not change.

Answer:

They do not change.