In the diagram above, O is the center of the circle, ∠UOT = 70 and ∠RST = 100. Calculate ∠RUO.

  • A 20°
  • B 25°
  • C 50°
  • D 80°
jamb 2005mathematics

The correct answer is B. 25°

∠OUT = ∠OTU = a (Base ∠s of 180 Δ)

∴ a + a + 70 = 180

(sum of ∠s of a Δ)

2a = 180- 70

2a = 110

a = 55

But ∠RUT + ∠RBT = 180

(opposite ∠s of a Cyclic quad)

∴ x + a = 100 = 180

x + 55 + 100 = 180

x = 180 - 155

x = 25

so ∠RUO = x = 25

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