Triangle ACB 'A=115°, 'C=25°, 'B= 40° What is the sum of the measures of the exterior angles of triangle ACB?
The sum of the measures of the exterior angles of any triangle is always 360 degrees.
To find the sum of the measures of the exterior angles of triangle ACB, we need to remember that the sum of the measures of all exterior angles of any polygon is always 360 degrees.
Now, in this case, we are given the measures of the interior angles A, B, and C. To find the measure of the exterior angle at any vertex, we subtract the corresponding interior angle from 180 degrees.
Let's calculate the exterior angles at each vertex:
At vertex A: Exterior angle at A = 180 - angle A = 180 - 115 = 65 degrees
At vertex B: Exterior angle at B = 180 - angle B = 180 - 40 = 140 degrees
At vertex C: Exterior angle at C = 180 - angle C = 180 - 25 = 155 degrees
Now, to find the sum of all exterior angles, we add them up:
Sum of the measures of the exterior angles = 65 + 140 + 155 = 360 degrees.
Therefore, the sum of the measures of the exterior angles of triangle ACB is 360 degrees.