Question

The points A, B, C, and D are taken in order on the circumference of a circle. Chords AC and BD intersect at point E. mABarc = 76° and mCDarc = 80°. Draw chord AD. Find m∠AEB.

Answer 1

• ∠AEB = 78°
• see attached for a drawing

Explanation:

The angle where the chords cross is the average of the two intercepted arcs:

∠AEB = (∠AOB +∠COD)/2 = (76° +80°)/2 = 78°

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Chord AD connects points A and D.