In the above figure, m∠AOC = 27° and m∠BOD = (2x + 37)°. If ∠AOC and ∠BOD are vertical angles, what is the value of x?
Vertical angles are congruent, meaning they have the same measure. Since m∠AOC = 27° and m∠BOD = (2x + 37)° are vertical angles, we can set them equal to each other:
27° = 2x + 37°
Subtract 37 from both sides to isolate 2x:
-10° = 2x
Divide by 2 to solve for x:
x = -5
Therefore, the value of x is -5.