In triangle ABC, angle B is 74 *. A circle is circumscribed around the triangle, and a tangent is drawn

In triangle ABC, angle B is 74 *. A circle is circumscribed around the triangle, and a tangent is drawn to the circle through point A. The CD beam forms an angle of 23 * with the AC side. Find the angles of triangle ACD.

Let’s build the radii OA, OB and OС.

The inscribed angle ABC, by condition, is 74 and rests on the arc AC, the central angle AOC also rests on the arc AC, then the degree measure of the arc AC = 2 * 74 = 148.

Since the AD is tangent, and the AC is a chord, the angle between them, the СAD angle, is equal to half of the AC arc

Then the angle СAD = 148/2 = 74.

Angle ADС = (180 – СAD – AСD) = (180 – 74 – 23) = 83.

Answer: The angles of the AСD triangle are 23, 74, 83.