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 ∠EFB?

Answer 1

Hi Leah,

Even though, you were not showing the circle with the two cords, you can look at you circle and mark your two arcs that are given. Notice that the two arc are opposite each other. You can use one of the circle theorems that says:

"If two chords intersect to form the the 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."

So if you add the two arcs together and divide by 2, you will find m<AFE or m<DFB. They are vertical angles and therefore congruent. Once you get this angle (40 + 70)/2 = 55, can you get m<EFB?

Think about supplementary angles and you will have it.

Glad to help,

Regina