Final answer:
The exterior angle associated with the given remote interior angles of 58 degrees and 62 degrees is 120 degrees. The measure of the third angle of the triangle is 60 degrees.
Step-by-step explanation:
To determine the measure of the exterior angle associated with the given remote interior angles of a triangle, we use the exterior angle theorem. The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles, also known as remote interior angles. With the given angles of 58 degrees and 62 degrees, we simply add them to find the exterior angle:
Exterior Angle = 58° + 62° = 120°
Next, to find the measure of the third angle of the triangle, we use the fact that the sum of all interior angles of a triangle is 180 degrees. Since we are already given two angles, we subtract their sum from 180 degrees:
Third Angle = 180° - (58° + 62°) = 180° - 120° = 60°