Question

Один из внешних углов треугольника равен 112 градусов. Углы не смежных с ним относятся как 2 к 5. Найти углы треугольника. дайти ответ срочнооо

Answer 1

Given Information:

We are given that one of the external angles of a triangle is 112 degrees, and the ratios of the non-adjacent angles to this angle are 2:5. We need to find the measures of the angles of the triangle.

Solution:

Let's denote the measure of the external angle as x. According to the given information, we have:

x = 112 degrees The sum of the measures of the internal angles of a triangle is always 180 degrees. Therefore, the sum of the measures of the other two angles can be expressed as:

2x + 5x = 180 degrees

Simplifying the equation, we get:

7x = 180 degrees

Solving for x, we find:

x = 180 degrees / 7 ≈ 25.71 degrees

Now, we can find the measures of the other two angles:

2x ≈ 2 * 25.71 degrees ≈ 51.43 degrees

5x ≈ 5 * 25.71 degrees ≈ 128.57 degrees

Therefore, the measures of the angles of the triangle are approximately:

Angle 1: 51.43 degrees

Angle 2: 112 degrees

Angle 3: 128.57 degrees

Please note that these values are approximate due to rounding.

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