In triangle ABC, the angle A is 46 degrees, the outside angle at the vertex B is 115 degrees.

| May 9, 2021 | education

In triangle ABC, the angle A is 46 degrees, the outside angle at the vertex B is 115 degrees. Find the degree measure of the angle C.

Let’s designate the external angle at the vertex B as DBC, then the angle DBC = 115 degrees. Angles B and DBC are adjacent angles and together they make up a flat angle that is 180 degrees. Then:
angle B + angle DBC = 180 degrees;
angle B + 115 degrees = 180 degrees;
angle B = 180 degrees – 115 degrees;
angle B = 65 degrees.
By the theorem on the sum of angles in a triangle (the sum of all interior angles of any triangle is 180 degrees), we find the degree measure of the angle C:
angle A + angle B + angle C = 180 degrees;
46 degrees + 65 degrees + angle C = 180 degrees;
angle C = 180 degrees – 111 degrees;
angle C = 69 degrees.
Answer: angle C = 69 degrees.



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