Question

question 2 of 10 what is the measure of $widehat{ac}$?

Explanation:

Step1: Identify arc - angle relationships

The measure of an arc is related to the central angle that subtends it.

Step2: Calculate the measure of $\overset{\frown}{DE}$

Given that the angle at the circumference subtended by $\overset{\frown}{DE}$ is $30^{\circ}$, the central - angle subtended by $\overset{\frown}{DE}$ is also $30^{\circ}$ (angle subtended by an arc at the center is equal to the angle subtended at the circumference when the angles are in the same segment).

Step3: Calculate the measure of $\overset{\frown}{AE}$

Since $\angle ABE = 90^{\circ}$, the measure of $\overset{\frown}{AE}$ is $90^{\circ}$ (angle subtended by an arc at the circumference is half of the central - angle, and here the central - angle corresponding to $\overset{\frown}{AE}$ is $180^{\circ}$ for the semi - circle formed by the diameter $BC$ and the chord $AE$).

Step4: Calculate the measure of $\overset{\frown}{AC}$

$\overset{\frown}{AC}=\overset{\frown}{AE}+\overset{\frown}{DE}$. Substituting the values, we have $\overset{\frown}{AC}=90^{\circ}+30^{\circ}=120^{\circ}$.

Answer:

A. $120^{\circ}$