Note: Figure not drawn to scale.

Question

In the above figure, m∠AOC = 21° and m∠BOD = (2x + 36)°. If ∠AOC and ∠BOD are vertical angles, what is the value of x?

Answer 1

If ∠AOC and ∠BOD are vertical angles, then they are congruent, meaning they have the same measure.

Therefore, 21° = (2x + 36)°.

Simplifying the equation, we have:
21 = 2x + 36

Subtracting 36 from both sides:
-15 = 2x

Now, dividing both sides by 2:
-7.5 = x

Therefore, the value of x is -7.5.