In a cyclic quadrilateral ABCD, the interior angle ∠A measures (3x - 10)° and the opposite interior angle ∠C measures (2x + 40)°. What is the numerical value of x?
Answer and explanation
Correct answer: B. 30
- Step 1: Circle theorem: Opposite angles of a cyclic quadrilateral are supplementary (sum to 180°). Step 2. Set up equation: (3x - 10) + (2x + 40) = 180. Step 3. Combine like terms: 5x + 30 = 180 => 5x = 150 => x = 30. Answer: 30. Why not the others: 25 gives sum 155 ≠ 180; 35 gives sum 205 ≠ 180; 20 gives sum 130 ≠ 180.
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