In triangle ABC, angle B = 90 degrees. A straight line is drawn through vertex C, which is parallel to side AB

In triangle ABC, angle B = 90 degrees. A straight line is drawn through vertex C, which is parallel to side AB and forms an angle of 36 degrees AC. Find the angles A and C.

Since, according to the condition, straight lines AB and CD are parallel, the angle ACD is equal to the angle BAC as criss-crossing angles at the intersection of parallel straight lines AB and CD of the secant AC.

Angle BAC = ACD = 36.

Triangle ABC is rectangular, in which the sum of acute angles is 90; angle ACB = (90 – BAC) = (90 – 36) = 54.

Answer: The angle BAC is 36, the angle ACB is 54.