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WAEC 2017 Mathematics · Question 39

An arc of a circle of radius 7.5cm is 7.5cm long. Find, correct to the nearest degree, the angle which the arc…

Question

An arc of a circle of radius 7.5cm is 7.5cm  long. Find, correct to the nearest degree, the angle which the arc subtends at the centre of the circle. [Take π=227\pi = \frac{22}{7}]

  1. A.29o^o
  2. B.57o^o
  3. C.65o^o
  4. D.115o^o

Answer: B. 57o^o

Explanation written with AI and checked against the answer key

Analyze the question: The arc length equals the radius (7.5 cm). We need the angle at the centre, to the nearest degree, using π = 22/7. Concept: Arc length = (θ/360) × 2πr, so θ = (arc length × 360) / (2πr). Solution: θ = (7.5 × 360) / (2 × (22/7) × 7.5) The 7.5 cancels: θ = 360 / (44/7) θ = 360 × 7 / 44 θ = 2520 / 44 θ = 57.27° To the nearest degree, θ ≈ 57°. Check: When arc length = radius, the angle is exactly 1 radian. 1 radian = 180/π = 180 × 7/22 ≈ 57.27°. Tip: If you see "arc length = radius," the angle is 1 radian, which is about 57.3° (or 57° to the nearest degree). Remembering this saves you time in the exam, as you don't even need the numbers.

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