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alina1380 [7]
3 years ago
14

∠ACE is formed by two secants intersecting outside of a circle. If minor arc BD = 25°, minor arc AB = 115°, and minor arc DE = 1

15°, what is the measure of ∠ACE?

Mathematics
2 answers:
Jlenok [28]3 years ago
8 0
Answer is 40 degrees 
VikaD [51]3 years ago
6 0

Answer:

m∠ACE=40\°

Step-by-step explanation:

we know that

The measurement of<u> the external angle</u> 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\°

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