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

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.

1. Let’s admit an angle КЕF х degrees.

2. Then the angle MEF will be x * 4 = 4x degrees.

3. Let’s compose the equation.

x + x + 4x = 180;

6x = 180;

x = 180/6 = 30;

x = 30;

4. KEF is 1/2 of the angle DEF, that is, DEF = x * 2 = 30 * 2 = 60 °.

5. Find MEF.

x * 4 = 30 * 4 = 120 °.

Answer: 60 ° and 120 °.