Question

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

Answer 1

Answer:

15.

$x = 20$

16.

$\angle BFH$ = $100\textdegree$

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

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17.

$x = 7$

18.

$\angle BFH$ = $68\textdegree$

Step-by-step 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 $x$:

$5x = 3x + 40$

$5x - 3x = 3x - 3x + 40$

$2x = 40$

$\frac{2x}{2} = \frac{40}{2}$

$x = 20$

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 $x$:

$16x = 4x + 84$

$16x - 4x = 4x - 4x + 84$

$12x = 84$

$\frac{12x}{12} = \frac{84}{12}$

$x = 7$

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 $\angle BFH$:

$\angle BFH$ = $68\textdegree$