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

m∠ACE=
`40\°`

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=
`(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=
`(1)/(2)(105\°-25\°)`

m∠ACE=
`40\°`