Question

Angle angle B is half the size of angle a the measure of angle C is equal to 1 less than 2 times the measure of angle B the sum of the angle a and angle B is 114 can the three angles form a triangle why or why not

Answer 1

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.