Question

explore the properties of inscribed angles by following these steps. 1. move point c and observe how the angle measures change. when \\(\overset{\frown}{ac}\\) changes, \\(m\angle abc\\) and \\(m\angle adc\\) do not change and are dropdown to each other. options: always equal, not equal. \\(m\overset{\frown}{ac} = 104^\circ\\) \\(m\angle abc = 52^\circ\\) \\(m\angle adc = 52^\circ\\)

Explanation:

Step1: Recall Inscribed Angle Theorem

Inscribed angles subtended by the same arc are equal. Here, $\angle ABC$ and $\angle ADC$ both subtend arc $\overset{\frown}{AC}$.

Step2: Analyze Given Measures

Given $m\angle ABC = 52^\circ$ and $m\angle ADC = 52^\circ$, and when $\overset{\frown}{AC}$ changes (but still the same arc for both angles), their measures remain equal as per the theorem. Also, from the first dropdown, we know their measures "do not change", so the relationship between them is "always equal".

Answer:

always equal