Angle ACO is 34. Its side CA touches the circle centered at point O. Find the degree value of the larger

Angle ACO is 34. Its side CA touches the circle centered at point O. Find the degree value of the larger arc AD of the circle enclosed inside this angle.

From the center of the circle O draw the radius to the point of tangency A. ∠CAO = 90 ° since the radius drawn to the point of tangency is perpendicular to the tangent.
1. Consider △ CAO: ∠CAO = 90 °, ∠ACO = 34 °.
By the theorem on the sum of the angles of a triangle:
∠CAO + ∠ACO + ∠AOC = 180 °;
90 ° + 34 ° + ∠AOC = 180 °;
∠AOC = 180 ° – 124;
∠AOC = 56 °.
2. ∠AOC and ∠AOD are adjacent, which means:
∠AOC + ∠AOD = 180 °;
56 ° + ∠AOD = 180 °;
∠AOD = 180 ° – 56 °;
∠AOD = 124 °.
3. The degree measure of the central ∠AOD is equal to the degree measure of the arc on which it rests. Since ∠AOD is based on the arc AD, then:
arc AD = ∠AOD;
arc AD = 124 °.
Answer: arc AD = 124 °.