Question

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?

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Help please!

Answer 1

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.

Note: 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

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

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