AC is a chord of a cirlce. If X and Y are the two points, on the circumference of the circle, lying on the same side of the chord AC  such that $$\angle AXC$$ = $$58^o$$, then what is the measure of $$2\angle AYC$$?​

Correct option is D

Given:
AC is a chord of a circle.
X and Y are points on the circumference on the same side of chord AC.
∠AXC = 58°
Concept Used:
Angles in the same segment of a circle are equal.
Solution:
Since X and Y are points on the circumference on the same side of chord AC, ∠AXC and ∠AYC are angles in the same segment.

Therefore, ∠AYC = ∠AXC.

Given ∠AXC = 58°, so ∠AYC = 58°.
2∠AYC = 2 $$\times$$​ 58° = 116°.