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°=90°
3 x degrees minus 75 degrees plus 106 degrees equals 90 degrees

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

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

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

Answer 1

Since angles 1 and 2 are vertical angles, they are equal. Therefore, we can set up the equation:

\[
m∠1 = m∠2
\]

This translates to:

\[
106° = (3x - 75)°
\]

From here, we can rewrite it in a clearer form:

\[
3x - 75 = 106
\]

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

\[
3x°−75°=106°
\]

So the answer is the second option:

**3x°−75°=106°**