Mathematics

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 = 70o and ∠RST = 100o. Calculate ∠RUO.
  • A.
    20o
  • B.
    25o
  • C.
    50o
  • D.
    80o
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