One of the inner corners of the triangle is 30 ° one of the outer corners is 60 °

One of the inner corners of the triangle is 30 ° one of the outer corners is 60 ° Find the remaining inner corners of the triangle.

The outer corners of a triangle are the corners adjacent to the corners of the triangle.

The sum of the outer and inner angles of a triangle at one vertex is 180º.

Since the external angle φ at the vertex ∠В is equal to 60º, then:

∠В = 180º – φ;

∠В = 180º – 60º = 120º.

Since the sum of all the angles of the triangle is 180º, and one of the internal angles (∠A) is 30º, then to calculate the unknown angle ∠C you need:

∠С = 180º – ∠А – ∠В;

∠С = 180º – 30º – 120º = 30º.

Answer: the angle ∠В is equal to 120º, the angle ∠С is equal to 30º.