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

January 29, 2021 | education

| **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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