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°

1 answer

To solve for \( x \) using the measures of the vertical angles, we know that vertical angles are congruent. Therefore, we can set the measures of the angles equal to each other:

\[ m∠1 = m∠2 \]

Substituting the given expressions, we have:

\[ 106° = (3x - 75)° \]

Now, to derive the equation based on the vertical angles, we will rearrange it as:

\[ 3x - 75 = 106 \]

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

\[ 3x° - 75° = 106° \]

Thus, the answer is:

3x°−75°=106°