Question

∠ACE is formed by two secants intersecting outside of a circle. If minor arc BD = 28°, minor arc AB = 112°, and minor arc DE = 112°, what is the measure of ∠ACE

Answer 1

We need to calculate major arc AE
arc AE + AB + BD + DE = 360°
arc AE + 112 + 28 + 112 = 360°
arc AE = 108°

From the attachment we can see Angle ACE = .5 * (AE -BD)
Angle ACE = .5 * (108 -28)
Angle ACE = .5 * (80)
Angle ACE = 40°

answer is C