Question

question 8 of 10 what is the measure of \\(\widehat{de}\\)?

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. $\angle ABC$ and $\angle DBE$ are vertical angles, so $\angle ABC=\angle DBE = 39^{\circ}$.

Step2: Use the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. For inscribed angle $\angle BAC$ with measure $41^{\circ}$, it intercepts arc $\overset{\frown}{BC}$. For inscribed angle $\angle BDE$ which intercepts arc $\overset{\frown}{DE}$, and since vertical - angles and the symmetry of the circle situation, the measure of arc $\overset{\frown}{DE}$ is equal to the measure of arc $\overset{\frown}{AC}$. So the measure of $\overset{\frown}{DE}$ is $41^{\circ}$.

Answer:

D. 41°