Question

Find the value of x using angle properties & the measure of

Answer 1

15.

`x = 20`

16.

`\angle BFH` =
`100\textdegree`

`\angle CBD` =
`100\textdegree` (if needed)

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17.

`x = 7`

18.

`\angle BFH` =
`68\textdegree`

Explanation:

15. The two following angles, which is
`\angle CBD` and
`\angle BFH`, are Corresponding Angles. Write an expression by using the following measurements from
`\angle CBD` and
`\angle BFH`. Then, solve the expression for the value of
`x`:

`\angle CBD` =
`5x`

`\angle BFH` =
`3x + 40`

`5x = 3x + 40`

Solve for
`x`:

`5x = 3x + 40`

`5x - 3x = 3x - 3x + 40`

`2x = 40`

`(2x)/(2) = (40)/(2)`

`x = 20`

16. After you have the value
`x` use it to find the actual measurements of both
`\angle CBD` and
`\angle BFH`, by applying
`x` to the following expressions from both
`\angle CBD` and
`\angle BFH` and solve them:

-The value of
`x`:

`x = 20`

-Solve for
`\angle CBD`:

`\angle CBD` =
`5x`

`5(20)`

`100`

-The actual measurement of
`\angle CBD`:

`\angle CBD` =
`100\textdegree`

-Solve for
`\angle BFH`:

`\angle BFH = 3x + 40`

`3(20) + 40`

`60 + 40`

`100`

-The actual measurement of
`\angle BFH`: (if needed)

`\angle BFH` =
`100\textdegree`

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17. The two following angles, which is
`\angle BFE` and
`\angle DBF` are Alternate Interior Angles .Write an expression by using the following measurements from
`\angle BFE` and
`\angle DBF`. Then, solve the expression for the value of
`x`:

`\angle BFE` =
`16x`

`\angle DBF` =
`4x + 84`

`16x = 4x + 84`

-Solve for
`x`:

`16x = 4x + 84`

`16x - 4x = 4x - 4x + 84`

`12x = 84`

`(12x)/(12) = (84)/(12)`

`x = 7`

18. After you have the value
`x` use it to find the actual measurement of
`\angle DBF`, by applying
`x` to the expression from
`\angle DBF` and solve it and find the actual measurement of an angle that is not labeled, which is
`\angle BFH`:

-The value of
`x`:

`x = 7`

Solve for
`\angle DBF`:

`\angle DBF` =
`4x + 84`

`4(7) + 84`

`28 + 84`

`112`

-The actual measurement of
`\angle DBF`:

`\angle DBF` =
`112\textdegree`

-Since both
`\angle DBF` and
`\angle BFH` are supplementary (two angles that equals to
`180\textdegree`), and you want to find the actual measurement of
`\angle BFH`, Use the measurement of
`\angle DBF` and subtract it from
`180\textdegree`:

`\angle DBF - 180\textdegree`

`112\textdegree - 180\textdegree = 68\textdegree`

-The actual measurement of
`\angle BFH`:

`\angle BFH` =
`68\textdegree`