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