Question

in the diagram below chords ab and cd intersect at e if mAEC =4x mAC=120 and mDB = 2x what is the value of x

Answer 1

• x = 20

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According to the Angles of Intersecting Chords Theorem, the angle between two chords is half the sum of the intercepted arc measures :

• m∠AEC = m∠DEB = (mAC + mDB)/2

Substitute and solve for x:

• 4x = (120 + 2x)/2
• 4x = 60 + x
• 3x = 60
• x = 20