Question

Circle O is shown. Chords B D and C A intersect at point E. Angle B E A is 112 degrees. The measure of arc B A is 120 degrees. The measure of arc C D is z.
What is the value of z?

52°
104°
116°
208°

Answer 1

When two chords intersect inside a circle, the measure of the angle formed is half the sum of the measures of the intercepted arcs. So

112 = 1/2 (arc BA + arc CD) = 1/2 (120 + z).

Multiply both sides by 2: 224 = 120 + z, so z = 104°.