The bisector EM of the acute angle E is drawn in the parallelogram FEOP. Point M on the segment OP.

| September 8, 2021 | education

The bisector EM of the acute angle E is drawn in the parallelogram FEOP. Point M on the segment OP. Find the sides and angles of a parallelogram if OP = 6 m, MP = 4 m and FEM angle is 22 degrees

Let us determine the length of the segment OM. OM = PO – RM = 6 – 4 = 2 m.

Since EM is the bisector of the angle FЕО, it cuts off the isosceles triangle ЕОМ, in which ЕО = ОМ = 2 m.

Since in a parallelogram the opposite sides are equal, then EO = FP = 2 m, PO = FE = 6 m.

Angle FEO = 2 * FEM = 2 * 22 = 44. The sum of adjacent angles of the parallelogram is 180, then the angle HJT = 180 – 44 = 136. The opposite angles of the parallelogram are equal, then the angle FPO = POE = 136.

Answer: The sides of the parallelogram are 2 m and 6 m, the angles of the parallelogram are 44 and 136.



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