Question

In triangle ABC,if measure of angle A is seven more than four times measure of angle B and measure of angle C is eleven more than measure of angle B,find the measure of angle A

Answer 1

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