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11111nata11111 [884]
3 years ago
15

AB and DE are chords that intersect at point F inside circle C as shown. If the measure of arc EA= 50 degrees and the measure of

arc DB= 70 degrees, what is the measure of angle AFE and angle EFB?
M
M
Help please!

Mathematics
1 answer:
defon3 years ago
8 0

Answer:

Part 1) m\angle AFE=55^o

Part 2) m\angle EFB=125^o

Step-by-step explanation:

Part 1) what is the measure of angle AFE

we know that

The measure of the interior angle is the semisum of the arches that comprise it and its opposite.

<u>Note:</u> In this problem the correct measure of arc EA is 40 degrees (see the picture)

so

m\angle AFE=\frac{1}{2}(arc\ EA+arc\ DB)

substitute the given values

m\angle AFE=\frac{1}{2}(40^o+70^o)=55^o

Part 2) what is the measure of angle  EFB?

we know that

m\angle AFE+m\angle EFB=180^o ---> by supplementary angles (form a linear pair)

so

substitute the given value

55^o+m\angle EFB=180^o

m\angle EFB=180^o-55^o=125^o

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