Secants BE and CF intersect at point A inside the circle.
Given that the measure of FAE = 60o and the measure of arc CE = 160 o, which is the measure of arc BF?

80
100
130
160

Question

Secants BE and CF intersect at point A inside the circle. 
Given that the measure of FAE = 60o and the measure of arc CE = 160 o, which is the measure of arc BF? 

80
100
130
160

anonymous · Answer

Use this theorem to solve.
If two secants intersect in the interior of a circle, then the measure of an angle formed is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

anonymous · Answer

i got it its 80 right

anonymous · Answer

yes

anonymous · Answer

i guessed

anonymous · Answer

OK, let's actually calculate it. Draw me a picture of a circle with two secants intersecting inside of the circle and then naming the angles.

anonymous · Answer

Are you drawing anything? I doesn't have to be pretty.

anonymous · Answer

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anonymous · Answer

Angle CAE = 180-60        Which is 120 degrees.   
Angle BAF is a vertical angle of angle CAE

So the sum of the arcs intercepted by angle CAE (160 deg) and vertical angle BAF  160 + M

So angle CAE is equal to one-half of 160 + M.

Which gets us 120=1/2(160 +M)

Which gets us 240=160 + M

So M = 80 degrees