Question

explore the properties of inscribed angles by following these steps. 1. move point c and observe how the angle measures change. when ac changes, m∠abc and m∠adc and are to each other. mac = 104° m∠abc = 52° m∠adc = 52°

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Given $m\widehat{AC}=104^{\circ}$, for inscribed angles $\angle ABC$ and $\angle ADC$ which intercept $\widehat{AC}$, we calculate their measures.

Step2: Apply the formula

$m\angle ABC=\frac{1}{2}m\widehat{AC}$ and $m\angle ADC = \frac{1}{2}m\widehat{AC}$. Since $m\widehat{AC}=104^{\circ}$, then $m\angle ABC = 52^{\circ}$ and $m\angle ADC=52^{\circ}$. When $\widehat{AC}$ changes, $m\angle ABC$ and $m\angle ADC$ change proportionally and are equal to each other.

Answer:

change proportionally; equal