Question

AB and DE are chords that intersect at point F inside circle C as shown. If the measure of arc EA = 40° and the measure of arc DB = 70°.

What is the measure of ∠AFE?

Select one or more:
a. 700
b. 400
c. 1250
d. 550

Answer 1

`d) \ 55\textdegree`

Explanation:

-we apply the relationship of chords intersecting within a circle:

-when two chords intersect to form a vertex of an angle within a circle, the measure of the angle is equal to one-half the sum of the measures of the two arcs intercepted by the angle and its vertical angle:

`\angle AFE=0.5(arc\ EA +arc \ BD)\\\\=0.5(40+70)\\\\=55\textdegree`

Hence, the measure of ∠AFE is 55°