Question

Дан Треугольник у которого угол 1 больше угла 2 на 20 градусов,а угол 2 меньше угла 3 на 20 градусов,найти углы

Answer 1

Пусть угол 2   =х°, тогда угол 1  =х°+20°, угол 3  =х°+20°
сумма углов Δ =180°, уравнение
х+20+х+х+20=180
3х=140°
х=140° :3=46 2/3    2 угол, 
46 2/3+20°=66 2/3 °   1 угол,
46 2/3+20°=66 2/3°  3 угол

Answer 2

Understanding the problem

You have a triangle with three angles, and you are given the following information: - Angle 1 is 20 degrees greater than angle 2. - Angle 2 is 20 degrees less than angle 3.

You need to find the measures of these three angles.

Solving the problem

Let's assign variables to the three angles: - Angle 1 will be represented by x. - Angle 2 will be represented by y. - Angle 3 will be represented by z.

Based on the given information, we can write the following equations: - x = y + 20 (equation 1) - y = z - 20 (equation 2)

To find the angles, we need to solve these two equations simultaneously.

Solving the equations

Let's substitute equation 2 into equation 1 to eliminate the variable y: - x = (z - 20) + 20 - Simplifying, we get: x = z

Now we have two equations with two variables: - x = z (equation 3) - y = z - 20 (equation 4)

Since equation 3 gives us a relationship between x and z, we can substitute this expression into equation 4 to solve for y: - y = z - 20 - y = x - 20 (substituting z with x, based on equation 3)

Now we have three equations with one variable, x: 1. x = z (equation 3) 2. y = x - 20 (equation 5) 3. x = y + 20 (equation 1)

To find the angles, we need to solve these equations.

Solving the system of equations

Let's start by substituting equation 1 into equation 5: - y = (y + 20) - 20 - Simplifying, we get: y = y

This equation tells us that y can be any value. Therefore, we cannot determine the exact measure of angle 2 based on the given information.

However, we can still find the relationship between the angles. From equation 1, we know that angle 1 (x) is 20 degrees greater than angle 2 (y): - x = y + 20

Since y can be any value, we can express angle 1 in terms of y: - x = y + 20

Similarly, from equation 3, we know that angle 3 (z) is equal to angle 1 (x): - z = x

Therefore, angle 3 can also be expressed in terms of y: - z = y + 20

Finally, we can express angle 2 in terms of y using equation 5: - y = y

To summarize, the relationships between the angles are as follows: - Angle 1 (x) = Angle 2 (y) + 20 degrees - Angle 2 (y) = Angle 2 (y) - Angle 3 (z) = Angle 2 (y) + 20 degrees

Since we do not have a specific value for angle 2, we cannot determine the exact measures of the angles in this triangle. However, we now know the relationships between the angles based on the given information.