Angles DEF and MEF are adjacent, ray EK is the bisector of angle DEF, angle KEF is 4 times

| June 22, 2021 | education

Angles DEF and MEF are adjacent, ray EK is the bisector of angle DEF, angle KEF is 4 times less than angle MEF. Find the corners DEF and MEF.

By the condition of the problem, it is specified that the angles DEF and MEF are adjacent, which means that their sum is 180 degrees. Beam EK is the bisector of the angle DEF, which means that the angle is divided in half. The KEF angle is 4 times smaller than the MEF angle. Since the value of any angle is not specified, we denote the KEF angle as x, then the FEM angle will be 2x. The angle DEK is equal to the angle KEF, which means that KED is also x. Let’s make the equation:

x + x + 4x = 180;

6x = 180;

x = 180: 6;

x = 30 (degrees) – angle KEF;

The angle DEF is the sum of the angles DEK and KEF, DEK = KEF, DEF = DEK + KEF = 30 + 30 = 60 (degrees).

MEF = 4 * 30 = 120 (degrees).

Answer: 60 degrees and 120 degrees.



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