SOLUTION: Hi, everyone. Can anyone help me with this question, please? Given: BD is a tangent to circle O at point C. The measure of arc EAC is 278, and the measure of angle ACB is 35. Fi

Question 1114906: Hi, everyone. Can anyone help me with this question, please?
Given: BD is a tangent to circle O at point C. The measure of arc EAC is 278, and the measure of angle ACB is 35. Find the measure of angle ACE.
Here is the link to the image: https://api.agilixbuzz.com/Resz/~6iS9DAAAAAghvTq664DvmA.0zTkW15fX0TSl0tGyYh46A/19791663,8C5/Assets/assessmentimages/geometry_part_2_u4l7_3.jpg
The answer choices are (a) 104, (b) 110, (c)121.5, and (d) none of these. I've done this several different ways, and gotten different answers. Immediate help would be greatly appreciated.
Thanks so much! :)
Answer by greenestamps(13208) (Show Source): You can put this solution on YOUR website!

Angle ACB with measure 35 degrees has its vertex on the circle, so the measure of arc ACB is 2*35 = 70 degrees.

It is given that arc AEC measures 278 degrees, so the measure of arc EFA is 278-70 = 208 degrees.

Arc EFA is the arc cut off by angle ACE, so the measure of angle ACE is 208/2 = 104 degrees.
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