In triangle ABC, angle B is 4 times and angle C is 7 times greater than angle A. Find all the angles of the triangle.

Let the degree measure of angle A be equal to x degrees, then the degree measure of angle B is equal to 4x degrees (if it is several times greater, then it is necessary to multiply), and the degree measure of angle C is equal to 7x degrees. According to the theorem on the sum of the angles of a triangle, the sum of the angles of a triangle ABC is equal to (x + 4x + 7x) degrees or 180 degrees. Let’s make an equation and solve it.

x + 4x + 7x = 180;

12x = 180;

x = 180: 12;

x = 15 ° – angle A;

4x = 15 * 4 = 60 ° – angle B;

7x = 15 * 7 = 105 ° – angle C.

Answer. ∠A = 15 °; ∠B = 60 °; ∠C = 105 °.

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