A triangle has one of the inner angles of 30 degrees and one of the outer angles of 40 degrees

A triangle has one of the inner angles of 30 degrees and one of the outer angles of 40 degrees. Find the rest of the interior corners of the triangle.

Since the sum of all the angles of the triangle is 180º, the angle ∠А is equal to 30º, then:

∠А + ∠В + ∠С = 180º;

∠В = 180º – ∠А – ∠С.

For this, we calculate the value of the angle ∠С. Since the sum of the outer and inner angles of the triangle is 180º, and the value of the outer angle at the vertex C is 40º, then:

∠С = 180º – φ;

∠С = 180º – 40º = 140º.

∠В = 180º – 140º – 30º = 10º.

Answer: the value of the angle ∠В is equal to 10º, the value of the angle ∠С is equal to 140º.