Given a circle with center $D$, if arc $\mathrm{BEC}$ subtends a central angle of $210°$, what is the measure of arc $\mathrm{BEC}$ in degrees?

• A. $210°$
• B. $150°$
• C. $209°$
• D. $134°$

Answer: (A)

Verified step by step guidance

1. Recall that a central angle in a circle is an angle whose vertex is at the center of the circle and whose sides intersect the circle, subtending an arc.
2. Understand that the measure of a central angle is equal to the measure of the arc it subtends. This is a fundamental property of circles.
3. Given that the central angle \( \angle BDC \) (where D is the center) measures 210\degree, the arc \( BEC \) subtended by this angle will have the same measure.
4. Therefore, the measure of arc \( BEC \) is equal to the measure of the central angle, which is 210\degree.
5. Conclude that the measure of arc \( BEC \) is 210\degree, matching the central angle's measure.