Question

explore the properties of inscribed angles by following these steps. 1. move point c and observe how the angle measures change. when $widehat{ac}$ changes, $mangle abc$ and $mangle adc$ and are to each other. always equal not equal check $mwidehat{ac}=104^{circ}$ $mangle abc = 52^{circ}$ $mangle adc = 52^{circ}$

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle in a circle is half the measure of the intercepted arc.

Step2: Analyze angles ∠ABC and ∠ADC

Both ∠ABC and ∠ADC intercept arc $\overset{\frown}{AC}$. Given $m\overset{\frown}{AC}=104^{\circ}$, then $m\angle ABC=\frac{1}{2}m\overset{\frown}{AC}$ and $m\angle ADC = \frac{1}{2}m\overset{\frown}{AC}$.

Answer:

always equal