Answer: Angle A is 115 degrees
Step-by-step explanation:
In triangle ABC, the measure of angle A is seven more than four times measure of angle B. This means that
Angle A = 4(Angle B) + 7
The measure of angle C is eleven more than measure of angle B. This means that
Angle C = Angle B + 11.
The equations are
A = 4B + 7 - - - - - - - - 1
C = B + 11 - - - - - - - - - - 2
Recall that the sum of the angles in a triangle is 180 degrees. This means that
A + B + C = 180 degrees
Substituting equation 1 and equation 2 into A + B + C = 180, it becomes
4B + 7 + B + B + 11 = 180
6B + 18 = 180
6B = 180 - 18 = 162
B = 162/6 = 27 degrees
Substituting B = 27 into equation 1, it becomes
A = 4×27 + 7 = 108 +7
A = 115 degrees
Substituting B = 27 into equation 2, it becomes
C = 27 + 11
C = 38 degrees
Sum of the angles is 115 + 27 + 38 = 180
