The bisector of the angle M of the parallelogram MPKC intersects the side PK at point B.

The bisector of the angle M of the parallelogram MPKC intersects the side PK at point B. Find the perimeter of the parallelogram if MP = 14, BK = 15 cm.

In the problem, we will use the properties of angles for parallel lines and a secant.
∠ РМВ = ∠ СМВ (MB – bisector by condition).
∠ CMB = ∠ РВM (internal crosswise lying with parallel MС, РK and secant MВ).
We got that there are two equal angles in the MРВ triangle: ∠ РМВ = ∠ РВМ – isosceles triangle.
MР = PB = 14 (cm).
Find the side of the РK of this parallelogram:
РK = РВ + BK = 14 + 15 = 29 (cm).
We find the perimeter of the parallelogram, it is equal to:
P MPKC = 2 * (14 + 29) = 86 (cm). Answer: 86 cm perimeter of the parallelogram.