Through the vertex M of the triangle MHK, a straight line AB is drawn, parallel to the side of the triangle HK

Through the vertex M of the triangle MHK, a straight line AB is drawn, parallel to the side of the triangle HK. At the same time, AMH = 64 degrees, BMК = 60 degrees. Determine which of the angles of the triangle will be the largest.

The angle of the MHK of the triangle is equal to the angle of the HMН as criss-crossing angles at the intersection of parallel lines AB and HK of the secant НM. Angle MHK = 60.

The angle MKH of the triangle is equal to the angle AMK as the intersecting angles at the intersection of parallel lines AB and HK of the secant KM. Angle MKH = 64.

Then the angle HMK = 180 – MHK – MKH = 60 – 64 = 56.

Answer: In a triangle, the MKH angle is the largest.