Question

3. In the diagram below, PO || RS. If mTVO = 5x – 22 and mVWS = 3x+ 10, what is the value of x? T Pt Q R+ -S W

Answer 1

According to the given diagram, angles TVO and VWS are corresponding angles by definition, which means they are congruent.

Having said that, we can express the following equation.

`m\angle TVO=m\angle VWS`

Let's replace the given expressions.

`5x-22=3x+10`

We subtract 3x from both sides.

`\begin{gathered} 5x-3x-22=3x-3x+10 \\ 2x-22=10 \end{gathered}`

Add 22 on both sides.

`\begin{gathered} 2x-22+22=10+22 \\ 2x=32 \end{gathered}`

At last, we divide the equation by 2.

`\begin{gathered} (2x)/(2)=(32)/(2) \\ x=16 \end{gathered}`

Therefore, x is equal to 16.