Question

There is a pair of vertical angles whose measures are m∠1=106°
and m∠2=(3x−75)°
. What equation can you write to solve for x
?(1 point)
Responses

3x°−75°−106°=180°
3 x minus 75 minus 106 degrees equals 180 degrees

3x°−75°+106°=180°
3 x minus 75 plus 106 degrees equals 180 degrees

3x°−75°=106°
3 x minus 75 equals 106 degrees

3x°−75°+106°=90°

Answer 1

Vertical angles are equal, which means that the measures of angles 1 and 2 are the same. Therefore, you can set the two angle measures equal to each other to write the equation:

\[
m∠1 = m∠2
\]

Substituting the given measures:

\[
106° = (3x - 75)°
\]

To solve for \( x \), you can rewrite this as:

\[
3x - 75 = 106
\]

This matches the answer option:

**3x°−75°=106°**

So, the correct equation to solve for \( x \) is:

**3x°−75°=106°**