A straight line is drawn through the vertex from the triangle ABC parallel to the bisector

A straight line is drawn through the vertex from the triangle ABC parallel to the bisector AM of the triangle and intersecting the line AB at point K. Find the angles of the triangle AKC if the angle BAC = 70

Since the segment AM is the bisector of the angle BAC, the angle CAM = BAC / 2 = 70/2 = 35.

According to the condition, the segment СK is parallel to the bisector AM, AC is the secant intersecting these parallel lines, then the angle ACK = CAM = 35, as lying crosswise.

The angles KAC and BAC are adjacent angles, the sum of which is 180, then the angle KAC = 180 – BAC = 180 – 70 = 110.

Then from the triangle ACK angle AKC = (180 – KAC – CAM) = (180 – 110 – 35) = 35.

Answer: The angles of the triangle AKC are equal to 35,35,110.