# The angle opposite the base of an isosceles triangle is 50 degrees. Find the outside angle at the base.

January 27, 2021 | education

| The triangle sum theorem says that the sum of the angles of any triangle is 180 degrees.

In an isosceles triangle, the angles at the base are equal (angle 1 = angle 3 = x), therefore:

x + angle 2 + x = 180 degrees;

2x + 50 degrees = 180 degrees;

2x = 130 degrees;

x = 65 degrees.

Angle 1 = Angle 2 = 65 degrees.

The outer base angle (angle 4) and the inner base angle are adjacent, so their sum is 180 degrees:

angle 3 + angle 4 = 180 degrees;

65 degrees + angle 4 = 180 degrees;

angle 4 = 115 degrees.

Answer: 115 degrees.

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.