Question

I need help with homework If angle CVD is 4x-72 and angle BVA is 2x+18, then the value of x is......Also find, angle CVD, angle DVA, angle AVB , angle BVC... I got the picture with the questions

Answer 1

Given,

`\begin{gathered} \angle CVD\text{ = 4x-72} \\ \angle AVB=2x+18 \end{gathered}`
`\angle CVD=\angle AVB\text{ (vertically opposite angles.)}`

That is,

`\begin{gathered} 4x-72=2x+18 \\ 2x=90 \\ x=45 \end{gathered}`

Therefore,

`\angle CVD=180-72=108`
`\begin{gathered} \angle DVA=180-\angle CVD\text{ (linear pair)} \\ =180-108 \\ =72 \end{gathered}`
`\begin{gathered} \angle AVB=2x+18 \\ =90+18 \\ =108 \end{gathered}`
`\begin{gathered} \angle BVC=\angle DVA\text{ (vertically opposite angles)} \\ \angle BVC=72 \end{gathered}`