Question

The measure of angle B in a triangle is 4 more than twice the measure of angle A. The measure of angle C is 30 less than 3 times the measure of angle A. Find the measure of each angle.

Answer 1

`A = 34(1)/(3)`

`B = 72(2)/(3)`

`C = 73`

Explanation:

Given

Shape: Triangle

`B = 4 + 2A`

`C = 3A - 30`

Required

Solve for A, B and C

Since the shape is a triangle,

`A + B +C = 180`

Substitute
`B = 4 + 2A` and
`C = 3A - 30` in
`A + B +C = 180`

`A + 4 + 2A + 3A - 30 = 180`

Collect Like Terms

`A + 2A + 3A = 180 + 30 - 4`

`6A = 206`

Solve for A

`A = 206/6`

`A = 34(1)/(3)`

Substitute
`A = 34(1)/(3)` in
`B = 4 + 2A`

`B = 4 + 2 * 34(1)/(3)`

`B = 4 + 2 * (103)/(3)`

`B = 4 + (206)/(3)`

`B = (12 + 206)/(3)`

`B = (218)/(3)`

`B = 72(2)/(3)`

Substitute
`A = 34(1)/(3)` in
`C = 3A - 30`

`C = 3 * 34(1)/(3) - 30`

`C = 3 * (103)/(3) - 30`

`C = 103 - 30`

`C = 73`