Find the angles of a triangle if their degree measures are 2: 3: 7.

Since the sum of all the angles of the triangle is 180º, and the angles are 2: 3: 7, then we express:

2x – degree measure ∠A;

3x – degree measure of angle ∠В;

7x – degree measure of the angle ∠С;

2x + 3x + 7x = 180;

12x = 180;

x = 180/12 = 15;

∠А = 2 · 15 = 30º;

∠В = 3 · 15 = 45º;

∠С = 7 · 15 = 105º.

Answer: the angles of the triangle are equal to 30º, 45º, 105º.