Question

Note: Figure not drawn to scale.


In the above figure, m∠AOC = 24° and m∠BOD = (2x + 38)°. If ∠AOC and ∠BOD are vertical angles, what is the value of x?
A.
x = -14
B.
x = 62
C.
x = -7
D.
x = 31

Answer 1

Since angles AOC and BOD are vertical angles, they are equal. Therefore, we can set their measures equal to each other:

\[
m\angle AOC = m\angle BOD
\]

Given that \(m\angle AOC = 24^\circ\) and \(m\angle BOD = (2x + 38)^\circ\), we can write the equation:

\[
24 = 2x + 38
\]

Now, we will solve this equation for \(x\):

1. Subtract 38 from both sides:

\[
24 - 38 = 2x
\]

This simplifies to:

\[
-14 = 2x
\]

2. Now, divide both sides by 2:

\[
x = -7
\]

Thus, the value of \(x\) is

\[
\boxed{-7}
\]

So the correct answer is C. \(x = -7\).