Question

how does the measure of ∠abd compare to the measure of ∠acd? explain your reasoning. which of the following is a correct response? the measure of ∠abd? is greater than the measure of ∠acd? because ab is shorter than bd. the measure of ∠abd? is less than the measure of ∠acd? because ab is shorter than bd. the measure of ∠abd? is twice of the measure of ∠acd? because bd is a the diameter. the measures of the angles are equal because the intercepted arc of both angles is the same. show hints

Explanation:

Step1: Recall inscribed - angle theorem

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

Step2: Analyze angles ∠ABD and ∠ACD

Angles ∠ABD and ∠ACD are inscribed angles that intercept the same arc $\overset{\frown}{AD}$.

Step3: Determine the relationship

Since they intercept the same arc $\overset{\frown}{AD}$, by the inscribed - angle theorem, the measure of ∠ABD is equal to the measure of ∠ACD.

Answer:

The measures of the angles are equal because the intercepted arc of both angles is the same.