Question
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°
Answers
GPT-4o mini
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°**
\[
m∠1 = m∠2
\]
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°**