The outside angle at the vertex A of triangle ABC is three times the inside angle at this vertex.

The outside angle at the vertex A of triangle ABC is three times the inside angle at this vertex. Find the sum of the inside angles B and C.

Let us express the inner angle at the vertex A, for which we will use the variable a.

Then, in accordance with the condition of the problem, the external angle at a given vertex can be expressed as 3a.

Since we know from the school curriculum in geometry that the sum of these two angles is always 180 °, then it is possible to write down an equation and determine what the internal angle at this vertex is:

a + 3a = 180;

4a = 180;

a = 45.

Let’s determine what the sum of the other two angles will be equal to:

180 – 45 = 135.

Answer: 135 °.