In a triangle, the angle at one vertex is 46 degrees, the outer angle at the other vertex

In a triangle, the angle at one vertex is 46 degrees, the outer angle at the other vertex is 127 degrees, find the third angle.

Since the sum of the outer and inner angles is 180 °, we find the 2nd angle of the triangle:

180 ° – 127 ° = 63 °.

Since the sum of the angles of a triangle is 180 °, the value of the 3rd angle is equal to the difference:

180 – 63 ° – 46 ° = 61 °.

Answer: the required angle is 61 °.