The outer angle of the triangle is 130 °, the two inner ones that are not adjacent

The outer angle of the triangle is 130 °, the two inner ones that are not adjacent to it are referred to as 2:11. Find all the inside and outside corners.

The outer corner of a triangle is the angle adjacent to its vertex, and they add up to an unfolded angle, the degree measure of which is 180º.

Since the outer angle is 130º, the value of the inner angle is:

∠В = 180º – 130º = 50º.

Since the sum of all the angles of the triangle is 180º, and the angles ∠A and ∠C are related as 2:11, we express this equation as follows:

2x – degree measure ∠A;

11x – degree measure ∠С;

2x + 11x + 50 = 180;

2x + 11x = 180 – 50;

13x = 130;

x = 130/13 = 10;

∠А = 2 ∙ 10 = 20º;

∠С = 11 ∙ 10 = 110º.

Thus, the external angle at the vertex ∠А is equal to:

∠1 = 180º – 20º = 160º;

The external angle at the vertex ∠С is equal to:

∠3 = 180º – 110º = 70º.

Answer: the inner angles of the triangle are 50º, 20º, 110º, the outer corners are 160º, 70º.