One acute angle of a right triangle is 86 degrees larger than the other. Find larger acute angle

From the condition, we know that one acute angle of a right-angled triangle is 86 ° 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 + 86).

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 + 86) = 180;

x + x = 180 – 90 – 86;

2x = 4;

x = 2 ° is the smaller acute angle of the triangle, and 86 + 2 = 88 ° is the larger acute angle of the triangle.

Answer: 88 °

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