Question

In the adjoining 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°