Question

∠E and ∠F are vertical angles with m∠E=9x+12 and m∠F=3x+24 . What is the value of x? Enter your answer in the box. x =

Answer 1

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 2

`x=2`

Explanation:

We have been given that ∠E and ∠F are vertical angles with
`m\angle E=9x+12` and
`m\angle F=3x+24`.

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:

`9x+12=3x+24`

`9x-3x+12=3x-3x+24`

`6x+12=24`

`6x+12-12=24-12`

`6x=12`

`(6x)/(6)=(12)/(6)`

`x=2`

Therefore, the value of x is 2.