In triangle ABC, angle B = 40 degrees. A straight line is drawn through vertex C, which is parallel to side AB

In triangle ABC, angle B = 40 degrees. A straight line is drawn through vertex C, which is parallel to side AB and forms an angle of 40 degrees with AC. Find the angles A and C in triangle ABC.

Since, according to the condition, the segment CD is parallel to the AC side, then the angle BAC = ACD as criss-crossing angles at the intersection of parallel lines AB and CD of the secant AC. Then the triangle ABC is isosceles, the angle ABC = BAC = 40, and the angle ACB = (180 – 40 – 40) = 100.

Answer: The angles of the triangle ABC are equal to 40, 40, 100.