In a triangle ABC, yr C = 30 °, and the outer angle at the apex A = 120 °. Find the unknown angles of the triangle.

Given: In a triangle ABC, angle C = 30 °, and the outer angle at the vertex A = 120 °. Find the unknown angles of the triangle.

Solution:

According to the condition, the angle at the vertex A is external, which means that it is equal to the sum of two angles that are not adjacent to it, i.e. angle A = angle C + angle B.

Find angle B = angle A-angle C = 120 ° -30 ° = 90 °.

The sum of the angles of a triangle is 180 °, which means yr. A = 180 ° – angle B – angle C = 180 ° -90 ° -30 ° = 60 °.

Answer: angle A = 60 °, angle B = 90 °.