Answer:
The value of x is 8
Step-by-step explanation:
In the figure below,
The alternate exterior angles are 1 and 2
Alternate Exterior Angles are a pair of angles that lie on the outer side of each of those two lines but on opposite sides of the transversal and they are equal
Also angle 2 and 3 are adjacent and supplementary angle and their sum is equal to 180 degrees
Given that
[tex]\angle 1 = (4x + 28)^{\circ}[/tex]
[tex]\angle 3 = (14x + 8)^{\circ}[/tex]
Now we know that
[tex]\angle 2 + \angle 3 = 180 ^{\circ}[/tex]
[tex]\angle 2 +(14x+8) = 180[/tex]
[tex]\angle 2 = 180 - 14x -8[/tex]
[tex]\angle 2 = 172 - 14x[/tex]
We also know that
[tex]\angle 1 = \angle 2[/tex]
[tex]4x + 28 = 172 -14x[/tex]
[tex]4x + 14x = 172 - 28[/tex]
[tex]18x = 144[/tex]
[tex]x =\frac{144}{18}[/tex]
x = 8
Now
[tex]\angle 1 = (4x+28)^{\circ} = (4(8) +28)^{\circ} = (32 +28)^{\circ} =(60)^{\circ}[/tex]
[tex]\angle 3= (14x+8)^{\circ} = (14(8) +8)^{\circ} = (112 +8)^{\circ} =(120)^{\circ}[/tex]
