Question

There is a pair of vertical angles whose measure are m<1 = 106 and m<2 = ( 3x - 75 ). What equation can u write to solve for x?

3x - 75 - 106 = 180

3x - 75 + 106 = 180

3x - 75 + 106 = 90

3x - 75 = 106

Answer 1

Vertical angles are equal, so we can set the measures of the angles equal to each other to solve for \( x \).

Given:

- Measure of angle 1: \( m\angle 1 = 106 \)
- Measure of angle 2: \( m\angle 2 = 3x - 75 \)

Since these angles are vertical angles, we have:

\[
m\angle 1 = m\angle 2
\]

This leads to the equation:

\[
106 = 3x - 75
\]

To solve for \( x \), you can rearrange this equation. None of the provided options perfectly match the standard way to write the equation, but the correct equation to start solving for \( x \) is essentially:

\[
3x - 75 = 106
\]

Thus, the correct choice from your options is:

**3x - 75 = 106**