In the above figure, m∠AOC = 21° and m∠BOD = (2x + 39)°. If ∠AOC and ∠BOD are vertical angles, what is the value of x?
Since ∠AOC and ∠BOD are vertical angles, they are equal in measure. Therefore, we have:
m∠AOC = m∠BOD
21° = 2x + 39°
Subtracting 39 from both sides of the equation, we get:
21° - 39° = 2x
-18° = 2x
Finally, dividing both sides of the equation by 2, we find:
-9° = x
Therefore, the value of x is -9.