One acute angle of a right triangle is 84 degrees larger than the other. Find a larger sharp corner.

From the condition, we know that one acute angle of a right-angled triangle is 84 ° larger than the other. In order to find the larger acute angle of a right-angled triangle, we compose and solve a linear equation with one variable.

Let’s introduce the variable x and denote it one of the acute angles of the triangle, then the second acute angle can be written as (x + 84).

From the theorem on the sum of the angles of a triangle, we know that the sum of the angles of a triangle is 180 °:

90 + x + (x + 84) = 180;

x + x = 180 – 90 – 84;

2x = 6;

x = 3 ° is the smaller acute angle of the triangle, and 84 + 3 = 87 ° is the larger acute angle of the triangle.

Answer: 87 °