One of the outer corners of the triangle is 15 degrees. The angles not adjacent to the given outer angle are 1: 4

One of the outer corners of the triangle is 15 degrees. The angles not adjacent to the given outer angle are 1: 4, find the largest of them.

In order to find the larger of the given angle, we will compose and solve the equation.

But first, let’s consider what we know from the condition.

It is known that one of the outer corners of a triangle is 15 °. It is also known that angles not adjacent to a given external angle are related as 1: 4.

According to the property, the outer angle of a triangle is equal to the sum of the inner angles that are not adjacent to it.

We introduce the coefficient of similarity k, then the non-adjacent angles are equal to 1k and 4k.

Let’s compose and solve the equation:

k + 4k = 15;

5k = 15;

k = 15: 5;

k = 3 coefficient of similarity.

So, the larger angle is 4 * 3 = 12 °.