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Marie asked in Science & MathematicsMathematics · 1 decade ago

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.


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!

1 Answer

  • 1 decade ago
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    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."

    Using your given numbers, your equation would be:

    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. ;)

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