M and K are the midpoints of sides AB and BC of triangle ABC. Find the MK and the BMK angle

M and K are the midpoints of sides AB and BC of triangle ABC. Find the MK and the BMK angle, if AC = 14 cm, the angle A is 72 degrees.

1.) First, find the value of MK.
By hypothesis, M and K are the midpoints of the sides AB and BC of the triangle ABC, respectively.
Thus, the segment MK is the midline of the triangle ABC.
As a rule, the middle line of the triangle is parallel to the third side, that is, the segment MK is parallel to the side AC.
Also, according to the rule, the length of the centerline of a triangle is equal to half the length of the side to which this centerline is parallel.
So it can be written.
MK = AC: 2.
MK = 14: 2.
MK = 7 (cm).
2.) Find the value of the angle BMK.
Since line AB intersects two parallel lines MK and AC, then, according to the rule, the corresponding angles are equal.
The angles BMK and BAC are corresponding in construction.
Angle A is also the angle BAC.
Thus, the BAC angle is equal to the BMK angle.
Hence, it is possible to write down.
BAC = BMK = 72 °.
Answer: MK = 7 cm; BMK = 72 °.