Question

сумма двух углов треугольника равна80градусов 1угол больше другого на 20 градусов. Чему равны углы треугольника?

Answer 1

Problem Analysis

We are given that the sum of two angles of a triangle is 80 degrees, and one angle is 20 degrees larger than the other. We need to find the measures of the angles of the triangle.

Solution

Let's assume that the measure of the smaller angle is x degrees. Since one angle is 20 degrees larger than the other, the measure of the larger angle is x + 20 degrees.

According to the given information, the sum of the two angles is 80 degrees. We can write this as an equation:

x + (x + 20) = 80

Simplifying the equation, we have:

2x + 20 = 80

Subtracting 20 from both sides, we get:

2x = 60

Dividing both sides by 2, we find:

x = 30

So, the measure of the smaller angle is 30 degrees, and the measure of the larger angle is 30 + 20 = 50 degrees.

Therefore, the angles of the triangle are 30 degrees, 50 degrees, and the third angle can be found by subtracting the sum of the other two angles from 180 degrees:

Third angle = 180 - (30 + 50) = 100 degrees.

Hence, the angles of the triangle are 30 degrees, 50 degrees, and 100 degrees.

Answer

The angles of the triangle are 30 degrees, 50 degrees, and 100 degrees.