Question
In the diagram, PQ is parallel to RS.
If angle UWS = 5x - 12 and angle QVU = 113, what is the value of x?
20
25
67
113
If angle UWS = 5x - 12 and angle QVU = 113, what is the value of x?
20
25
67
113
Answers
There are no human answers yet.
Answered by
GPT-4o mini
Since PQ is parallel to RS, we can use the properties of angles formed by parallel lines to find the value of \( x \).
From the given information:
- Angle \( UWS = 5x - 12 \)
- Angle \( QVU = 113 \)
Since PQ is parallel to RS and \( UWS \) and \( QVU \) are alternate interior angles, they are equal. Therefore, we can set up the equation:
\[
5x - 12 = 113
\]
Now we solve for \( x \):
1. Add 12 to both sides:
\[
5x = 113 + 12
\]
\[
5x = 125
\]
2. Divide by 5:
\[
x = \frac{125}{5} = 25
\]
Thus, the value of \( x \) is \( \boxed{25} \).
From the given information:
- Angle \( UWS = 5x - 12 \)
- Angle \( QVU = 113 \)
Since PQ is parallel to RS and \( UWS \) and \( QVU \) are alternate interior angles, they are equal. Therefore, we can set up the equation:
\[
5x - 12 = 113
\]
Now we solve for \( x \):
1. Add 12 to both sides:
\[
5x = 113 + 12
\]
\[
5x = 125
\]
2. Divide by 5:
\[
x = \frac{125}{5} = 25
\]
Thus, the value of \( x \) is \( \boxed{25} \).
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