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