# 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.

Let x ° be the third corner of the triangle;

Then (x + 15) ° is the second corner of the triangle;

Then (x + 15 + 45) ° is the first corner of the triangle;

The sum of the angles of a triangle is always 180 °, so let’s make and solve the equation:

x + (x + 15) + (x + 15 + 45) = 180;

3x + 75 = 180;

3x = 180 – 75;

3x = 105;

x = 105/2;

x = 52.5 ° – third angle;

(x + 15) ° = 52.5 + 15 = 67.5 ° – the second angle;

Then (x + 15 + 45) ° = 52.5 + 15 + 45 = 112.5 ° is the first angle.

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