Answer:
[tex]\boxed {x = 4}[/tex]
[tex]\boxed {\angle 1 = 41\textdegree}[/tex]
[tex]\boxed {\angle 2 = 139\textdegree}[/tex]
[tex]\boxed {\angle 3 = 41\textdegree}[/tex]
[tex]\boxed {\angle 4 = 139\textdegree}[/tex]
Step-by-step explanation:
Both [tex]\angle 1[/tex] and [tex]\angle 3[/tex] are Vertical Angles. So, to the find actual measurement both of angles, you need to write an expression by using the following measurements labeled on both [tex]\angle 1[/tex] and [tex]\angle 3[/tex], and solve for [tex]x[/tex]:
[tex]\angle 1 = 8x + 9[/tex]
[tex]\angle 3 = 14x - 15[/tex]
[tex]8x + 9 = 14x - 15[/tex]
-Solve:
[tex]8x + 9 = 14x - 15[/tex]
[tex]8x + 9 - 14x = 14x - 14x - 15[/tex]
[tex]-6x + 9 = -15[/tex]
[tex]-6x + 9 = -15 - 9[/tex]
[tex]-6x = -24[/tex]
[tex]\frac{-6x}{-6} = \frac{-24}{-6}[/tex]
[tex]\boxed {x = 4}[/tex]
After you have the value of [tex]x[/tex], use it to find the actual measurement of [tex]\angle 1[/tex]and [tex]\angle 3[/tex]:
-The value of [tex]x[/tex]:
[tex]x = 4[/tex]
-Finding the measurement of [tex]\angle 1[/tex]:
[tex]8x + 9[/tex]
[tex]8(4) + 9[/tex]
[tex]32 + 9[/tex]
[tex]41[/tex]
[tex]\boxed {\angle 1 = 41\textdegree}[/tex]
-Finding the measurement of [tex]\angle 3[/tex]:
[tex]14x - 15[/tex]
[tex]14(4) - 15[/tex]
[tex]56 - 15[/tex]
[tex]41[/tex]
[tex]\boxed {\angle 3 = 41\textdegree}[/tex]
After you have the actual measurements of [tex]\angle 1[/tex] and [tex]\angle 3[/tex], find the actual measurements of [tex]\angle 2[/tex] and [tex]\angle 4[/tex]. [tex]\angle 1[/tex] and [tex]\angle 2[/tex] are both supplementary (two angle that add up to [tex]180\textdegree[/tex]), you need to find the measurement of [tex]\angle 2[/tex] by subtracting the measurement of [tex]\angle 1[/tex] from [tex]180\textdegree[/tex]. Same thing for [tex]\angle 3[/tex] and [tex]\angle 4[/tex]:
-Finding the measurement of [tex]\angle 2[/tex]:
[tex]180\textdegree - \angle 1[/tex]
[tex]180\textdegree - 41\textdegree[/tex]
[tex]139\textdegree[/tex]
[tex]\boxed {\angle 2 = 139\textdegree}[/tex]
-Finding the measurement of [tex]\angle 4[/tex]:
[tex]180\textdegree - \angle 3[/tex]
[tex]180\textdegree - 41\textdegree[/tex]
[tex]139\textdegree[/tex]
[tex]\boxed {\angle 4 = 139\textdegree}[/tex]
And were done.
