In triangle ABC, angle A is 42 more than angle C, and angle B is 48. Determine the magnitude of angles A and C.

Let the angle C be equal to x degrees, then the angle A is equal to (x + 42) degrees, and the angle B is equal to 48 °. By the theorem on the sum of the angles of a triangle: The sum of the angles of a triangle is 180 °, we get ∠A + ∠B + ∠C = 180 °. By the condition of the problem, the sum of the angles of the triangle ABC is (x + (x + 42) + 48) degrees or 180 °. Let’s make an equation and solve it.

x + (x + 42) + 48 = 180;

x + x + 42 + 48 = 180;

2x + 90 = 180;

2x = 180 – 90;

2x = 90;

x = 90: 2;

x = 45 ° – angle С;

x + 42 = 45 + 42 = 87 ° – angle A.

Answer. ∠C = 45 °; ∠A = 87 °.