Question

∠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?

Answer 1

Answer is 40 degrees 

Answer 2

Answer:

m∠ACE=$40\°$

Step-by-step explanation:

we know that

The measurement of the external angle is the semi-difference of the arcs which comprises

In this problem

m∠ACE represent a external angle

so

m∠ACE=$\frac{1}{2}(minor\ arc\ AE- minor\ arc\ BD)$

Find the minor arc AE

$minor\ arc\ AE=360\°-minor\ arc\ AB-minor\ arc\ BD-minor\ arc\ ED$

substitute the values

$minor\ arc\ AE=360\°-115\°-25\°-115\°=105\°$

m∠ACE=$\frac{1}{2}(105\°-25\°)$

m∠ACE=$40\°$