Question

Ray VD bisects angle CVE. m angle CVD=20x+4, and m angle EVD=14x+22. Solve for x, and give the angle measures for all three angles.

Answer 1

We know that

• Ray VD bisects angle CVE.

,

• Angle CVD = 20x+4

,

• Angle EVD = 14x+22

If VD bisects CVE, then angle CVD and EVD are equal, that means

`\begin{gathered} m\angle CVD=m\angle EVD \\ 20x+4=14x+22 \end{gathered}`

Now, we solve for x. First, we subtract 4 on each side

`\begin{gathered} 20x+4-4=14x+22-4 \\ 20x=14x+18 \end{gathered}`

Then, we subtract 14x on each side

`\begin{gathered} 20x-14x=14x+18-14x \\ 6x=18 \end{gathered}`

At last, we divide the equation by 6

`\begin{gathered} (6x)/(6)=(18)/(6) \\ x=3 \end{gathered}`

With this value, we find each angle.

`m\angle CVD=20x+4=20(3)+4=60+4=64`
`m\angle EVD=14x+22=14(3)+22=42+22=64`

Therefore, each angle measures 64°, and the whole angle CVE measures 128°.