ABCD is a cyclic quadrilateral in which $∠ A = 6 7^{\circ}$ and $∠ B = 9 2^{\circ}$ . What is the difference between the measures of $∠ C$ and $∠ D$ ?

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Question

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Answer 1

Given:

ABCD is a cyclic quadrilateral

∠A = 67°

∠B = 92°

Formula used:

In a cyclic quadrilateral, the opposite angles are supplementary:

∠A + ∠C = 180°

∠B + ∠D = 180°

Difference between ∠C and ∠D = |∠C - ∠D|

Calculations:

∠A + ∠C = 180°

⇒ ∠C = 180° - 67° = 113°

∠B + ∠D = 180°

⇒ ∠D = 180° - 92° = 88°

Difference between ∠C and ∠D = |∠C - ∠D|

⇒ Difference = |113° - 88°|

⇒ Difference = 25°

∴ The correct answer is option (4).

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