In the diagram, PQ is parallel to RS.

Question

If angle UWS = 5x - 12 and angle QVU = 113, what is the value of x?

20
25
67
113

Answer 1

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 $\boxed{{\displaystyle 25}}$.