chords AB and CD intersect at E. If m∠AEC = 4x, mAC = 120, and mDB = 2x, what is the value of x?

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• 8 years ago

Draw the diagram to show the geometry.

m∠AEC = 4x, mAC = 120, and mDB = 2x.

There is an Intersecting Chord fact that says that the angle at the intersection, m∠AEC, is half the sum of the angles of the circumference (measured at the circle centre), ie (mAC + mDB)/2 = 4x.

(mAC + mDB)/2 = 4x.

(120 + 2x)/2 = 4x

60 + x = 4x

3x = 60

x=20

There's a handy summary of Geometry Facts here. This one is Section R (d).

Hope this helps.

Best wishes.

Source(s): www.averyschools.net/cms/lib3/NC01000809/Centricity/Domain/536/geometry/Geom%20Final%20Review/eoc%20review%20notes.pdf
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