Question
There is a pair of vertical angles whose measures are ∡1=106° and ∡2=(3x−75)° . Which equation would you use to solve for x ?(1 point)
Responses
3x−181=1803 x minus 181 is equal to 180
3x+31=1803 x plus 31 is equal to 180
3x−75=1063 x minus 75 is equal to 106
3x+31=903 x plus 31 is equal to 90
Responses
3x−181=1803 x minus 181 is equal to 180
3x+31=1803 x plus 31 is equal to 180
3x−75=1063 x minus 75 is equal to 106
3x+31=903 x plus 31 is equal to 90
Answers
Answered by
GPT-4o mini
To solve for \( x \) using the fact that vertical angles are equal, we can set the measures of the two angles equal to each other.
Given:
- \( \angle 1 = 106^\circ \)
- \( \angle 2 = (3x - 75)^\circ \)
Since these are vertical angles, we can write the equation:
\[
3x - 75 = 106
\]
This equation is not listed among the options provided, but since the goal is to determine the structure of the equation based on the information given, the closest relevant choice from your provided options would be:
**3x - 75 = 106**
This option is represented by:
**3x - 75 = 106** (though this specific option is not present in your list).
If we strictly need to select an answer based on the responses, unfortunately none of the presented options accurately describe the required equation. However, the logic leads to the equation \( 3x - 75 = 106 \) to find the value of \( x \).
Given:
- \( \angle 1 = 106^\circ \)
- \( \angle 2 = (3x - 75)^\circ \)
Since these are vertical angles, we can write the equation:
\[
3x - 75 = 106
\]
This equation is not listed among the options provided, but since the goal is to determine the structure of the equation based on the information given, the closest relevant choice from your provided options would be:
**3x - 75 = 106**
This option is represented by:
**3x - 75 = 106** (though this specific option is not present in your list).
If we strictly need to select an answer based on the responses, unfortunately none of the presented options accurately describe the required equation. However, the logic leads to the equation \( 3x - 75 = 106 \) to find the value of \( x \).