Question

In figure, chords AC and DE intersect at B. If ∠ABE = 108°, m(arc AE) = 95°, find m(arc DC).

Answer 1

Chords AC and DE intersect internally at point B.

∴ ∠ABE = `1/2` [m(arc AE) + m(arc DC)]

∴ 108° = `1/2` [95° + m(arc DC)]

∴ 108° × 2 = 95° + m(arc DC)

∴ 95° + m(arc DC) = 216°

∴ m(arc DC) = 216° − 95°

∴ m(arc DC) = 121°