Question

In triangle ABC, the measure of angle B is 33 more than three times the measure of angle A. The measure of angle C is 57 more than the measure of angle A. Find the measure of each angle.

Answer 1

a= 18

b=87

​c=75

Explanation:

1. We will use Gaussian elimination to solve this problem.

b= 33+3a

c= 57+a

a+b+c= 180

2. Swap Row1 and Row3 to make row reduction easier.

a+b+c=180

-a+c=57

-3a+b=33

3. Apply to Row2 : Row2 + Row1.

a+b+c=180

b+2c=237

-3a+b=33

4. Apply to Row3 : Row3 + 3 Row1.

a+b+c=180

b+2c=237

4b+3c=573

5. Apply to Row3 : Row3 - 4 Row2.

a+b+c=180

b+2c=237

-5c=-375

6. Simplify rows.

a+b+c=180

b+2c=237

c=75

7. Apply to Row2 : Row2 - 2 2 Row3.

a+b+c=180

b=87

c=75

8. Apply to Row1 : Row1 - Row3.

a+b=105

b=87

c=75

9. Apply to Row1 : Row1 - Row2.

a=18

b= 87

c= 75

10. Simplify rows.

a=18

b= 87

c=75

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