From the cyclic quadrilateral MNOP above, find the value of x.

  • A 16°
  • B 25°
  • C 42°
  • D 39°

The correct answer is C. 42°

In a cyclic quadrilateral, the opposite angles are supplementary. That is, the sum of opposite angles is 180°.

(2x + 18)° + 84° = 180°

2x + 102° = 180° ⟹2x = 78°

x = 39°

In the given diagram, we have:

\(x + 90° + 50° + 25° = 180°\).

Simplify and solve for x:

\(x = 180° - 165° = 15°\).

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