Answer:
The measure of angle 5 is 75 degrees
Step-by-step explanation:
when two parallel line are cut by a traversal then we have vertical angles corresponding angles, alternate angles , supplementary angle and so on..
Here in the attached figure
5 and 8 are vertical angles and they are equal.
Similarly angle 6 and 7 are also vertical angles and they are equal
So
-9x -12 = 6x + 183
Grouping the like terms
-9x -6x = 183 + 12
-15x = 195
[tex]x = \frac{ 195}{15}[/tex]
x = -13
Thus angle 7 is
= -9(-13) -12
= 117 -12
= 105
Now angle 7 and angle 5 are supplementary angles i.e., they sum is 180 degrees
[tex]\angle 7 +\angle 5 = 105^{\circ}[/tex]
[tex]105^{\circ} + \angle 5 = 180^{\circ}[/tex]
[tex]\angle 5 = 180^{\circ} - 105^{\circ}[/tex]
[tex]\angle 5 = 75^{\circ}[/tex]
