Question
In the diagram, PQ is parallel to RS.
If angle UWS = 5x - 12 and angle QVU = 113, what is the value of x?
If angle UWS = 5x - 12 and angle QVU = 113, what is the value of x?
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the value of \( x \), we can use the properties of parallel lines and transversals. Since \( PQ \) is parallel to \( RS \), angles \( UWS \) and \( QVU \) are corresponding angles.
According to the problem, we have:
\[
\angle UWS = 5x - 12
\]
\[
\angle QVU = 113
\]
Since these angles are corresponding angles, we can set them equal to each other:
\[
5x - 12 = 113
\]
Next, we will solve for \( x \):
1. **Add 12 to both sides:**
\[
5x - 12 + 12 = 113 + 12
\]
\[
5x = 125
\]
2. **Divide both sides by 5:**
\[
x = \frac{125}{5}
\]
\[
x = 25
\]
Thus, the value of \( x \) is \( \boxed{25} \).
According to the problem, we have:
\[
\angle UWS = 5x - 12
\]
\[
\angle QVU = 113
\]
Since these angles are corresponding angles, we can set them equal to each other:
\[
5x - 12 = 113
\]
Next, we will solve for \( x \):
1. **Add 12 to both sides:**
\[
5x - 12 + 12 = 113 + 12
\]
\[
5x = 125
\]
2. **Divide both sides by 5:**
\[
x = \frac{125}{5}
\]
\[
x = 25
\]
Thus, the value of \( x \) is \( \boxed{25} \).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.