Answer: No, the angles cannot form a triangle.
Step-by-step explanation:
Angle angle B is half the size of angle A. This means that
A = 2B
The measure of angle C is equal to 1 less than 2 times the measure of angle B. This means that
C = 2B - 1
The sum of the angle A and angle B is 114. This means that
A+B = 114
Substituting A = 2B into (A+B = 114), it becomes
2B + B = 114
3B = 114
B = 114/3 = 38 degrees
A = 114 - 38 = 76
C = 2B - 1
C = 2×38 - 1 = 76 - 1
C = 75
Recall, sum of angles in a triangle is 180 degrees. This means that
A + B+ C = 180 degrees. T
Therefore, if we add add angle A, angle B and angle C, it becomes
76 + 38 + 75 = 189 degrees
The sum is more than the sum of the angles in a triangle. Therefore, the angles cannot form a triangle.
