In the above figure, m∠AOC = 24° and m∠BOD = (2x + 37)°. If ∠AOC and ∠BOD are vertical angles, what is the value of x?

Question

A.
x = -6.5
B.
x = -13
C.
x = 61
D.
x = 30.5

Answer 1

Since ∠AOC and ∠BOD are vertical angles, they are equal. Thus, we can set up the equation:

\[ m∠AOC = m∠BOD \]

Substituting the given values:

\[ 24° = (2x + 37)° \]

Now, we can solve for \(x\).

1. Subtract 37 from both sides:

\[ 24 - 37 = 2x \]

\[ -13 = 2x \]

2. Divide both sides by 2:

\[ x = -\frac{13}{2} \]

3. Simplify:

\[ x = -6.5 \]

So the value of \(x\) is:

\[ \boxed{-6.5} \]

Thus, the correct answer is A. \(x = -6.5\).