Question

Circle D is inscribed with triangle A B C. The measure of arc A B is 76 degrees. Point E is on the circle between points B and C.

What is the measure of arc BEC in circle D?

134°
150°
209°
210°

Answer 1

I can’t answer uniquely as written — there isn’t enough information about point E. All we know (arc AB = 76°) gives angle C = 38°, but the measure of arc BEC (the arc from B to C that passes through E) depends on where E is placed on the arc BC (or which arc BC you mean: minor or major) or on any extra condition (for example “E is the midpoint of arc BC”, or “AE is an angle bisector”, or a given angle/length).

Could you post the diagram or give the missing condition that defines E (for example, “E is the midpoint of arc BC,” “AE is a diameter,” “AE bisects ∠A,” etc.)? With that I can find the correct choice and show the work.