Answer:
15.
[tex]x = 20[/tex]
16.
[tex]\angle BFH[/tex] = [tex]100\textdegree[/tex]
[tex]\angle CBD[/tex] = [tex]100\textdegree[/tex] (if needed)
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17.
[tex]x = 7[/tex]
18.
[tex]\angle BFH[/tex] = [tex]68\textdegree[/tex]
Step-by-step explanation:
15. The two following angles, which is [tex]\angle CBD[/tex] and [tex]\angle BFH[/tex], are Corresponding Angles. Write an expression by using the following measurements from [tex]\angle CBD[/tex] and [tex]\angle BFH[/tex]. Then, solve the expression for the value of [tex]x[/tex]:
[tex]\angle CBD[/tex] = [tex]5x[/tex]
[tex]\angle BFH[/tex] = [tex]3x + 40[/tex]
[tex]5x = 3x + 40[/tex]
Solve for [tex]x[/tex]:
[tex]5x = 3x + 40[/tex]
[tex]5x - 3x = 3x - 3x + 40[/tex]
[tex]2x = 40[/tex]
[tex]\frac{2x}{2} = \frac{40}{2}[/tex]
[tex]x = 20[/tex]
16. After you have the value [tex]x[/tex] use it to find the actual measurements of both [tex]\angle CBD[/tex] and [tex]\angle BFH[/tex], by applying [tex]x[/tex] to the following expressions from both [tex]\angle CBD[/tex] and [tex]\angle BFH[/tex] and solve them:
-The value of [tex]x[/tex]:
[tex]x = 20[/tex]
-Solve for [tex]\angle CBD[/tex]:
[tex]\angle CBD[/tex] = [tex]5x[/tex]
[tex]5(20)[/tex]
[tex]100[/tex]
-The actual measurement of [tex]\angle CBD[/tex]:
[tex]\angle CBD[/tex] = [tex]100\textdegree[/tex]
-Solve for [tex]\angle BFH[/tex]:
[tex]\angle BFH = 3x + 40[/tex]
[tex]3(20) + 40[/tex]
[tex]60 + 40[/tex]
[tex]100[/tex]
-The actual measurement of [tex]\angle BFH[/tex]: (if needed)
[tex]\angle BFH[/tex] = [tex]100\textdegree[/tex]
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17. The two following angles, which is [tex]\angle BFE[/tex] and [tex]\angle DBF[/tex] are Alternate Interior Angles .Write an expression by using the following measurements from [tex]\angle BFE[/tex] and [tex]\angle DBF[/tex]. Then, solve the expression for the value of [tex]x[/tex]:
[tex]\angle BFE[/tex] = [tex]16x[/tex]
[tex]\angle DBF[/tex] = [tex]4x + 84[/tex]
[tex]16x = 4x + 84[/tex]
-Solve for [tex]x[/tex]:
[tex]16x = 4x + 84[/tex]
[tex]16x - 4x = 4x - 4x + 84[/tex]
[tex]12x = 84[/tex]
[tex]\frac{12x}{12} = \frac{84}{12}[/tex]
[tex]x = 7[/tex]
18. After you have the value [tex]x[/tex] use it to find the actual measurement of [tex]\angle DBF[/tex], by applying [tex]x[/tex] to the expression from [tex]\angle DBF[/tex] and solve it and find the actual measurement of an angle that is not labeled, which is [tex]\angle BFH[/tex]:
-The value of [tex]x[/tex]:
[tex]x = 7[/tex]
Solve for [tex]\angle DBF[/tex]:
[tex]\angle DBF[/tex] = [tex]4x + 84[/tex]
[tex]4(7) + 84[/tex]
[tex]28 + 84[/tex]
[tex]112[/tex]
-The actual measurement of [tex]\angle DBF[/tex]:
[tex]\angle DBF[/tex] = [tex]112\textdegree[/tex]
-Since both [tex]\angle DBF[/tex] and [tex]\angle BFH[/tex] are supplementary (two angles that equals to [tex]180\textdegree[/tex]), and you want to find the actual measurement of [tex]\angle BFH[/tex], Use the measurement of [tex]\angle DBF[/tex] and subtract it from [tex]180\textdegree[/tex]:
[tex]\angle DBF - 180\textdegree[/tex]
[tex]112\textdegree - 180\textdegree = 68\textdegree[/tex]
-The actual measurement of [tex]\angle BFH[/tex]:
[tex]\angle BFH[/tex] = [tex]68\textdegree[/tex]
