# The largest angle of an acute-angled triangle is five times the smallest. Find the angles

The largest angle of an acute-angled triangle is five times the smallest. Find the angles of this triangle, if you know that they are all expressed as an integer number of degrees.

Let’s designate a smaller angle x, then the larger one will be 5 * x.

The angles in a triangle add up to 180 °. So the average angle is:
180 – (5 * x + x) = 180 – 6 * x.

By condition, our triangle is acute-angled. This means that the largest angle is less than 90 °.
Let’s compose 1 inequality:
5 * x <90 °;
x <18 °.

The middle angle should be less than the large one. Let’s compose 2 inequalities:
180 – 6 * x <5 * x;
11 * x> 180 °.
x> 16.36 °.

16.36 ° <x <18 °.
x = 17 °.

5 * x = 17 * 5 = 85 °.
180 – (17 + 85) = 78 °.

Answer: The angles of the triangle are 17 °, 78 ° and 85 °. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.