Algebra 2 practice

Question

The sum of the angles in a triangle is 180 .in triangle abc if c is equal to the sum of the other angles and b is equal to 5a-c what are the measures of the angles a b c

Answer 1

Let A , B , and C be the angles of the triangle. You need to solve the system

A + B + C = 180

A + B = C

5 A - C = B

and you will find A = 30 , B = 60 , and C =90

Answer 2

This question involves system of equations with three variables (a, b, c)

Step 1:

From given, we can construct three equations:

c=a+b

b=5a-c

a+b+c=180

Step 2:

Rewrite these equations into right order:

a+b-c=0

5a-b-c=0

a+b+c=180

Step 3:

Put these equations into augmented matrix, and then using Gaussian elimination method to solve a, b, c.

⌈1,1,-1,0; 5,-1,-1,0; 1,1,1,180⌋ →(-5)*R1+R2 and (-1)*R1+R3→⌈1,1,-1,0; 0,-6,4,0; 0,0, 2, 180⌋

a+b-c=0

-6b+4c=0

2c=180

Step 4: solve for c first, and then solve for b, and lastly for a.

2c=180→c=90

-6b+4(90)=0→b=60

a+60-90=0→a=30

Finished!