In triangle ABC, angle B is 90 degrees; angle A is 10 degrees greater than angle C. Find angle A and angle C.

From the condition we know that in the triangle ABC the angle B is equal to 90 °, the angle A is more than the angle C by 10 °. In order to find the angle A and the angle C of the triangle, we compose and solve a linear equation with one variable.

We denote by the variable x the degree measure of the angle C, then the degree measure of the angle A can be written as (x + 10) °.

Let us recall and apply the theorem on the sum of the angles of a triangle. It says that the sum of the angles of the triangle is 180 °.

90 + x + x + 10 = 180;

2x = 180 – 90 – 10;

2x = 80;

x = 40 ° is equal to the angle C, then the angle A is 40 + 10 = 50 °.