Question

Кути DEF і MEF– суміжні промінь EK – бісектриса кута DEF, кут KEF на 57° менший від кута MEF. Знайдіть кути DEF і MEF. Пожалуйста помогите, срочно!!!!!!!​

Answer 1

Объяснение:

Сума  суміжних кутів 180°,тоді

MEF-KEF= 78° (за умовою),тоді MEF=KEF+78° .

DEF=2*KEF(за умовою,так як промінь EK – бісектриса кута DEF).

Отримані вирази підставляємо у формулу

DEF + MEF=DEМ= 180°, 2*KEF+KEF+78° = 180°, 3*KEF=180°--78° ,3*KEF=102°,

KEF=102°÷3=34°

DEF=2*KEF=2*34°=68°

MEF=180°-68°=112°.

Answer 2

Problem Analysis

We are given that DEF and MEF are adjacent rays, and EK is the bisector of angle DEF. We are also given that angle KEF is 57° less than angle MEF. We need to find the measures of angles DEF and MEF.

Solution

Let's denote the measure of angle DEF as x. Since EK is the bisector of angle DEF, we know that angle DEK is equal to angle KEF, and angle EFK is equal to angle KEF.

According to the given information, angle KEF is 57° less than angle MEF. Therefore, angle MEF can be expressed as (angle KEF + 57°).

Since angle DEK is equal to angle KEF, we can write the equation:

x = angle DEK = angle KEF

Similarly, angle EFK is equal to angle KEF, so we can write the equation:

angle EFK = angle KEF

Now, let's substitute the values into the equation for angle MEF:

(angle KEF + 57°) = angle MEF

Since angle DEK + angle EFK + angle MEF = 180° (the sum of angles in a triangle), we can write the equation:

x + x + (angle KEF + 57°) = 180°

Simplifying the equation:

2x + angle KEF + 57° = 180°

Substituting x = angle KEF:

2(angle KEF) + angle KEF + 57° = 180°

Combining like terms:

3(angle KEF) + 57° = 180°

Subtracting 57° from both sides:

3(angle KEF) = 180° - 57°

3(angle KEF) = 123°

Dividing both sides by 3:

angle KEF = 123° / 3

angle KEF = 41°

Since angle KEF = x, we have:

angle DEF = angle KEF = 41°

angle MEF = angle KEF + 57° = 41° + 57° = 98°

Therefore, the measures of angles DEF and MEF are 41° and 98°, respectively.

Answer: The measure of angle DEF is 41°, and the measure of angle MEF is 98°.