One corner of the triangle is 45 ° more than the second, and the third is 15 ° less than the second.

One corner of the triangle is 45 ° more than the second, and the third is 15 ° less than the second. Find the corners of the triangle.

In order to find the angle of a triangle, we will use the theorem on the sum of the angles of a triangle.

From the condition, we know that one corner of the triangle is 45 ° more than the second, and the third is 15 ° less than the second angle.

Let us denote by the variable x ° the value of the second angle, then we will write the first in the form (x + 45) °, and the third (x – 15) °.

The sum of the angles of the triangle is 180 °, we compose and solve a linear equation with one variable.

x + x + 45 + x – 15 = 180;

3x + 30 = 180;

3x = 180 – 30;

3x = 150;

x = 150: 3;

x = 50 ° second angle,

50 + 45 = 95 ° first corner,

50 – 15 = 35 ° third angle.