The vertical angles are congruent (have the same measures).
Therefore you have the equation:
∠E = ∠F → 9x + 12 = 3x + 24 |-12
9x = 3x + 12 |-3x
6x = 12 |:6
x = 2
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
We have been given that ∠E and ∠F are vertical angles with [tex]m\angle E=9x+12[/tex] and [tex]m\angle F=3x+24[/tex].
We know that vertical angles are equal in measure. To solve for x, we will equate measure of angle E to measure of angle F as:
[tex]9x+12=3x+24[/tex]
[tex]9x-3x+12=3x-3x+24[/tex]
[tex]6x+12=24[/tex]
[tex]6x+12-12=24-12[/tex]
[tex]6x=12[/tex]
[tex]\frac{6x}{6}=\frac{12}{6}[/tex]
[tex]x=2[/tex]
Therefore, the value of x is 2.
