Marie
Lv 4

# Can someone help me with this math question? It requires the drawing of a circle..?

Chords AB and CD intersect at E. If the measure of <AEC=4, and measure of Arc AC=120 and measure of arc DB=2x what is the value of X. Can anyone explain how they came to this answer please.

Update:

Oh im sorry there is a mistake <AEC=4X not 4

Update 2:

Oh im sorry there is a mistake <AEC=4X not 4

thanks a lot to Marly though i figured it out based on your first couple of steps, you were right there was a typo and i got x=30 now..thanks for all the help!

Relevance

There must be a typo here. The measure of angle AEC cannot equal 4 if arc AC is 120. The theorem you want to use is:

"If two chords intersect within a circle, then the measure of the angle formed is equal to one-half the sum of the measures of the intercepted arc."

4 = 1/2 (120 + 2x)

4 = 60 + 2x

2x = -56

x = -28

and, obviously, x cannot be negative! so something is wrong.

Hope this helps you figure it out, though. ;)