The ABC triangle is isosceles with the AC base. The line MK is parallel to the base (M belongs to BC, K belongs to AB).

The ABC triangle is isosceles with the AC base. The line MK is parallel to the base (M belongs to BC, K belongs to AB). Find the angles of the CME triangle if the angle B = 56 °, the angle C = 62 °.

1) Straight MK || AC Angle K and angle C- corresponding => Angle C = angle K = 62 degrees (By the property of parallel lines)
2) Straight MK || AC Angle K and angle M – one-sided => The sum of the angles K and M = 180 degrees (By the property of parallel lines)
3) Angle K + Angle M = 180 degrees => Angle M = 180 – 62 = 118
Answer: Angle B = 56 degrees; Angle K = 62 degrees; Angle M = 118 degrees