In the diagram above, O is the center of the circle,

∠UOT = 70o and ∠RST = 100o. 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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