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In the figure shown, m∠XOV = 47° and m∠UOW = (2x + 35)°. If ∠UOW and ∠XOV are vertical angles, what is the correct equation that could be used to solve for x?

A.
(2x)° = 47°
B.
(2x + 47)° = 35°
C.
(2x + 35)° = 47°
D.
(x + 35)° = 47°

1 answer

Since ∠UOW and ∠XOV are vertical angles, their measures are equal. Given that:

  • m∠XOV = 47°
  • m∠UOW = (2x + 35)°

We can set these two angles equal to each other:

\[ (2x + 35)° = 47° \]

Thus, the correct equation to solve for \(x\) is:

C. \((2x + 35)° = 47°\)