In the diagram above, O is the center of the circle,
∠UOT = 70º and ∠RST = 100º. Calculate ∠RUO.
Attached Figure / Diagram
A
20o
B
25o
C
50o
D
80o
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
∠OUT = ∠OTU = a (Base ∠s of 180 \Delta)
∴ a + a + 70 = 180o (sum of ∠s of a \Delta)
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
Source: Myschool Past Questions Archive (Record #8425)