In the diagram above O is the center of the cir... - JAMB Mathematics 2005 Question

∠OUT = ∠OTU = a (Base ∠s of 180 Δ)

∴ a + a + 70 = 180^o (sum of ∠s of a Δ)

2a = 180^o - 70^o

2a = 110^o

a = 55^o

But ∠RUT + ∠RBT = 180^o (opposite ∠s of a Cyclic quad)

∴ x + a = 100 = 180

x + 55 + 100 = 180

x = 180 - 155

x = 25

so ∠RUO = x = 25^o