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

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

Correct Answer: Option B

Explanation

∠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