Question

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

Answer 1

We know, if two chords of a circle intersect each other in the interior of a circle, then the measure of the angle between them is half the sum of measures of the arcs intercepted by the angle and its opposite angle.

∴ ∠ABE = $\frac{1}{2}$[m(arc AE) + m(arc DC)]

⇒ m(arc AE) + m(arc DC) = 2∠ABE

⇒ 95º + m(arc DC) = 2 × 108º

⇒ m(arc DC) = 216º − 95º = 121º

Thus, the measure of arc DC is 121º.