Given a circle with center O and points E and H on the circumference such that the central angle $\angle EOH$ measures $114°$, what is the measure of arc EH?

• A. $114°$
• B. $228°$
• C. $246°$
• D. $123°$

Answer: (A)

Verified step by step guidance

1. Recall that the measure of a central angle in a circle is equal to the measure of the arc it intercepts. This means the central angle \( \angle EOH \) corresponds directly to arc \( EH \).
2. Identify the given central angle measure: \( \angle EOH = 114^\circ \).
3. Since the central angle and the intercepted arc have the same measure, the measure of arc \( EH \) is also \( 114^\circ \).
4. Understand that the entire circle measures \( 360^\circ \), so the remaining arc (the arc not intercepted by \( \angle EOH \)) would be \( 360^\circ - 114^\circ = 246^\circ \).
5. Therefore, the measure of arc \( EH \) is the same as the central angle \( \angle EOH \), which is \( 114^\circ \).