Question

Найти углы треугольника ABC,если B на 40 градусов меньше угла С,и на 20 больше угла A

Answer 1

С=в+40
А=в-20
3в+20=180
В=160/3=53+1/3
С=93+1/3
А=33+1/3

Answer 2

I can help you with your math question. Let me explain how to find the angles of the triangle ABC.

First, we need to use the fact that the sum of the angles in any triangle is 180 degrees. That means that $$A + B + C = 180$$

Next, we need to use the given information about the angles. We know that $$B = C - 40$$ and $$B = A + 20$$. We can substitute these expressions into the first equation and get:

$$A + (C - 40) + C = 180$$ $$A + 2C - 40 = 180$$

Now we can solve for C by adding 40 to both sides and dividing by 2:

$$A + 2C = 220$$ $$2C = 220 - A$$ $$C = \frac{220 - A}{2}$$

To find A, we can use the second equation that relates B and A:

$$B = A + 20$$ $$A = B - 20$$

We can substitute the expression for B in terms of C:

$$A = (C - 40) - 20$$ $$A = C - 60$$

Now we have expressions for A and C in terms of each other. We can plug in either one into the equation for C and solve for the angle:

$$C = \frac{220 - A}{2}$$ $$C = \frac{220 - (C - 60)}{2}$$ $$C = \frac{280 - C}{2}$$ $$2C = 280 - C$$ $$3C = 280$$ $$C = \frac{280}{3}$$

This is the value of the angle C in degrees. To find A, we can plug in this value into the expression for A:

$$A = C - 60$$ $$A = \frac{280}{3} - 60$$ $$A = \frac{100}{3}$$

This is the value of the angle A in degrees. To find B, we can use either of the equations that relate B to A or C:

$$B = A + 20$$ $$B = \frac{100}{3} + 20$$ $$B = \frac{160}{3}$$

This is the value of the angle B in degrees. Therefore, the angles of the triangle ABC are:

$$A = \frac{100}{3}^\circ$$ $$B = \frac{160}{3}^\circ$$ $$C = \frac{280}{3}^\circ$$

You can check that these values satisfy the given conditions and the sum of the angles is 180 degrees.

I hope this explanation was helpful. If you want to learn more about how to calculate angles, you can visit [this website](https://ru.wikihow.com/%D0%B2%D1%8B%D1%87%D0%B8%D1%81%D0%BB%D1%8F%D1%82%D1%8C-%D1%83%D0%B3%D0%BB%D1%8B) or use [this calculator](https://www.petrovskov.ru/resheniya/treugolnik.html).