Question

∠1 and ∠2 are vertical angles. If m∠1 = (5x + 12)° and m∠2 = (6x - 11)°. What is m∠2?

Answer 1

`\boxed {\angle 2 = 127\textdegree}`

Explanation:

First, you need to write an expression by using the following measurements from both
`\angle 1` and
`\angle 2`, and solve for
`x`:

`\angle 1 = 5x + 12`

`\angle 2 = 6x - 11`

`5x + 12 = 6x - 11`

Solve for
`x`:

`5x + 12 = 6x - 11`

`5x + 12 - 6x = 6x - 6x - 11`

`-x + 12 = -11`

`-x + 12 - 12 = -11 - 12`

`-x = -23`

`(-x)/(-1) = (-23)/(-1)`

`x = 23`

After you have the value of
`x`, use the value of
`x` and the expression from
`\angle 2` to get the actual measurement of
`\angle 2`:

-The value of
`x`:

`x = 23`

`\angle 2 = 6x - 11`

Solve for
`\angle 2`:

`6x - 11`

`6(23) - 11`

`138 - 11`

`127`

The measurement of
`\angle 2`:

`\boxed {\angle 2 = 127\textdegree}`