Answer: angle A = 63.3 degrees
angle B = 78.3 degrees
angle C = 38.3 degrees
Step-by-step explanation:
In triangle ABC, the measure of angle A is twenty-five degrees more than the measure of angle C. This means that
angle A = angle C + 25 degrees
The measure of angle B is 40 degrees more than the measure of angle C. This means that
angle B = angle C + 40
The equations are
A = C + 25 - - - - - - - -1
B = C + 40 - - - - - - - - - 2
Recall, the sum of angles in a triangle is 180 degrees. Therefore,
A + B + C = 180 - - - - - - 3
Substituting equation 1 and equation 2 into equation 3, it becomes
C + 25 + C + 40 + C = 180
3C + 65 = 180
3C = 180 - 65 = 115
C = 115/3 = 38.3 degrees
Substituting C = 38.3 into equation 1 and equation 2, it becomes
A = 38.3 + 25 = 63.3 degrees
B = 38.3 + 40 = 78.3 degrees
Sum of angle A, angle B and angle C = 63.3 + 78.3 +38.3 = 79.9 degrees.
Approximately 180 degrees
