Question

Углы DEF и MEF- смежные, луч EK- бесектриса угла DEF, угол KEF на 78 градусов меньше угла MEF. найдите углы DEF и MEF. помогите пожалуйста!!!!!!!!!!!!!!????????????

Answer 1

DEF + MEF = 180°, т.к. сумма смежных углов равна 180°
KEF = DEF/2, т.к. KEF - биссектриса  =>   DEF = KEF * 2
MEF = KEF + 78° - по условию задачи

Решаем уравнение
KEF * 2 + KEF + 78° = 180°
3KEF = 102°
KEF = 34°
DEF = 34° * 2 = 68°
MEF = 34° + 78° = 112°
проверка: DEF + MEF = 68 + 112 = 180°

Ответ: DEF = 68°
          MEF = 112°

Answer 2

Angles DEF and MEF

To find the measures of angles DEF and MEF, we are given the following information: - Angles DEF and MEF are adjacent angles. - Ray EK is the angle bisector of angle DEF. - Angle KEF is 78 degrees less than angle MEF.

Let's break down the problem step by step.

Step 1: Understanding the given information

Adjacent angles are angles that share a common vertex and a common side but do not overlap. In this case, angles DEF and MEF are adjacent angles.

An angle bisector is a line or ray that divides an angle into two congruent angles. In this case, ray EK is the angle bisector of angle DEF.

Step 2: Setting up the equation

Let's assume the measure of angle DEF is x degrees. Since ray EK is the angle bisector of angle DEF, angle KEF will also measure x degrees.

According to the given information, angle KEF is 78 degrees less than angle MEF. Therefore, the measure of angle MEF will be (x + 78) degrees.

Step 3: Solving the equation

We can now set up an equation based on the information we have:

x + 78 = x + 78

Simplifying the equation, we find that x = 0.

Step 4: Finding the measures of angles DEF and MEF

Since x = 0, the measure of angle DEF is 0 degrees.

To find the measure of angle MEF, we substitute x = 0 into the equation:

MEF = x + 78 = 0 + 78 = 78 degrees.

Therefore, the measure of angle DEF is 0 degrees, and the measure of angle MEF is 78 degrees.

I hope this helps! Let me know if you have any further questions.