One corner of the triangle is 45 degrees greater than the second, and the third is 15 degrees

One corner of the triangle is 45 degrees greater than the second, and the third is 15 degrees less than the second. find the corners of the triangle.

In order to find the angles of a triangle, we will compose and solve equations. To compose the equation, we will use the theorem on the sum of the angles of a triangle, which says that the sum of the angles of a triangle is 180 °.

We introduce the variable x °, denoting the degree measure of the second angle, then the first angle can be written as (x + 45) °, then the third angle can be written as (x – 15) °.

We compose a linear equation:

x + (x + 45) + (x – 15) = 180;

x + x + 45 + x – 15 = 180;

3x = 180 – 45 + 15;

3x = 150;

x = 150: 3;

x = 50 ° the second angle, then 50 + 45 = 95 °, and the third 50 – 15 = 35 °.