The vertices A, B, C and D of a quadrilateral ABCD lied on a circle. ∠A is thrice ∠C and ∠D is twice ∠B. What is the difference between the measures of ∠B and ∠C?
Show answer & explanation
Correct answer: B
Explanation
Correct Answer is option 2 i.e. 15°
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Concept |
Understanding |
Application |
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Sum of opposite angles of a cyclic quadrilateral is 180. |
Suppose ∠C = x and ∠B = y Then, ∠A = 3x and ∠D = 2y
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Now, ∠A + ∠C = 180 ⇒ x + 3x = 180 ⇒ x = 45 ∠B + ∠D = 180 ⇒ y + 2y = 180 ⇒ y = 60 Hence, ∠B – ∠C = y – x = 60 – 45 = 15° |