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Choose the Correct Alternative: - Geometry

MCQ

Four alternative answers for the following question is given. Choose the correct alternative. 

∠ACB is inscribed in arc ACB of a circle with centre O. If ∠ACB = 65°, find m(arc ACB).

Options

  • 65°

  • 130°

  • 295°

  • 230°

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Solution 1



The measure of an inscribed angle is half of the measure of the arc intercepted by it.

∴∠ACB = \[\frac{1}{2}\] m(arc AB)

⇒ m(arc AB) = 2∠ACB = 2 × 65º = 130º

∴ m(arc ACB) = 360º − m(arc AB) = 360º − 130º = 230º

Hence, the correct answer is 230° .

Solution 2

230°

Concept: Inscribed Angle
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