∠ACE is formed by two secants intersecting outside of a circle. If minor arc BD = 25°, minor arc AB = 115°, and minor arc DE = 115°, what is the measure of ∠ACE?
Accepted Solution
A:
Answer:m∠ACE = 40°Step-by-step explanation:Consider the below figure attached with this question.Given information: arc BD = 25°, minor arc AB = 115°, and minor arc DE = 115°.We need to find the measure of ∠ACE.minor arc AB + minor arc BD + minor arc DE + minor arc AE = 360°115° + 25° + 115° + minor arc AE = 360°255° + minor arc AE = 360°minor arc AE = 360° - 255°minor arc AE = 105°The measure of minor arc AE is 105°.Using Intersecting secants outside the circle theoremAngle between two secants = [tex]\frac{1}{2}[/tex](Major arc - Minor arc)[tex]\angle ACE=\frac{1}{2}[Arc(AE)-Arc(BD)][/tex][tex]\angle ACE=\frac{1}{2}[105-25][/tex][tex]\angle ACE=\frac{1}{2}[80][/tex][tex]\angle ACE=40[/tex]Therefore, the measure of ∠ACE is 40°.