Question

Луч MK делит угол AMB на два угла, причем угол AMK : угол KMB = 3 : 4. Найди вели-чины углов AMK и KMB, если угол AMB = 70°.помогите решить с пояснениями

Answer 1

возьмем углы как 3x   и 4x  тогда в сумме они дают  70

3x+4x=70

7x=70

x=10

3*10=30  АМК

4*10=40   КМВ

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer 2

Пусть х -1 часть угла АМВ

тогда 3х - АМК

4х-КМВ

АМК+ КМВ = АМВ

3х+4х=70

7х=70

х=10

3*1=30- угол АМК

4*10=40 - угол КМВ

Ответ: 30, 40

Answer 3

Problem Analysis

We are given that line segment MK divides angle AMB into two angles, with the ratio of the measures of angle AMK to angle KMB being 3:4. We are also given that the measure of angle AMB is 70°. We need to find the measures of angles AMK and KMB.

Solution

Let's denote the measure of angle AMK as 3x and the measure of angle KMB as 4x. We know that the sum of the measures of angles AMK and KMB is equal to the measure of angle AMB.

So, we have the equation: 3x + 4x = 70°

Solving for x: 7x = 70° x = 10°

Now we can find the measures of angles AMK and KMB: Angle AMK = 3x = 3 * 10° = 30° Angle KMB = 4x = 4 * 10° = 40°

Therefore, the measure of angle AMK is 30° and the measure of angle KMB is 40°.

Final Answer

The measure of angle AMK is 30° and the measure of angle KMB is 40°.