Question

The sum of interior angles in a triangle are 180 degrees. Angle B and C are congruent. Angle B is twenty less than angle A. Write and solve a system of equations using substitution. Write and solve a system to determine the measure of angles A, B, and C.

Answer 1

`A = (220)/(3)`

`B = (160)/(3)`

`C = (160)/(3)`

Explanation:

Given

`A + B + C = 180`

`B = C`

`B = A- 20`

Required

Solve for A, B and C

The equation binding A, B and C have been written out (above)

Substitute C for B in
`A + B + C = 180`

`A + B + B = 180`

`A + 2B = 180`

Substitute A - 20 for B

`A + 2(A - 20) = 180`

`A + 2A - 40 = 180`

`3A - 40 = 180`

Solve for 3A

`3A = 180 + 40`

`3A = 220`

`A = (220)/(3)`

Solve for B in
`B = A- 20`

`B = (220)/(3) - 20`

`B = (220 - 60)/(3)`

`B = (160)/(3)`

Recall that
`B = C`

`C = (160)/(3)`