In the diagram above, O is the center of the circle, &ang;UOT = 70º and &ang;RST...

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

Mathematics

JAMB 2005

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

∠UOT = 70º and ∠RST = 100º. Calculate ∠RUO.

A. 20^o
B. 25^o
C. 50^o
D. 80^o

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Correct Answer: Option B

Explanation

∠OUT = ∠OTU = a (Base ∠s of 180 Δ)
∴ a + a + 70 = 180o (sum of ∠s of a Δ)
2a = 180o - 70o
2a = 110o
a = 55o
But ∠RUT + ∠RBT = 180o (opposite ∠s of a Cyclic quad)
∴ x + a = 100 = 180
x + 55 + 100 = 180
x = 180 - 155
x = 25
so ∠RUO = x = 25o

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