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 plus 106 degrees equals 180 degrees

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

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

3x°−75°+106°=90°

Answer 1

Vertical angles are angles that are opposite each other when two lines intersect. They are always equal in measure. In this case, if \( m∠1 = 106° \) and \( m∠2 = (3x - 75)° \), then we can set the two angles equal to each other:

\[
106° = 3x - 75°
\]

To solve for \( x \), you can rearrange this equation.

However, in the responses you provided, the correct equation to write based on the vertical angles would be:

\[
3x - 75° = 106°
\]

So the correct answer is:

**3x°−75°=106°**
(3 x minus 75 equals 106 degrees)