Multiple choice

ΔABC is inscribed in a circle with center O, such that ∠ACB = 115°, O is joined to A. What is the measure of ∠OAB?

  1. 35°

  2. 20°

  3. 30°

  4. 25°
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a cyclic quadrilateral, opposite angles sum to 180°. ∠ACB = 115° is the angle subtended by arc AB. Central angle for same arc = 2 × 115° = 230°, but this exceeds 180°. Actually, ∠AOB = 2∠ACB = 230° reflex, so ∠AOB (minor) = 130°. In isosceles ΔAOB: ∠OAB = (180° - 130°)/2 = 25°.

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