In the diagram above, O is the center of the circle,
∠UOT = 70° and ∠RST = 100°. Calculate ∠RUO.
A.
20°
B.
25°
C.
50°
D.
80°
Correct Answer: 25°
Explanation
∠OUT = ∠OTU = a (Base ∠s of 180 Δ)
∴ a + a + 70 = 180° (sum of ∠s of a Δ)
2a = 180° - 70°
2a = 110°
a = 55°
But ∠RUT + ∠RBT = 180° (opposite ∠s of a Cyclic quad)
∴ x + a = 100 = 180
x + 55 + 100 = 180
x = 180 - 155
x = 25
so ∠RUO = x = 25°
∠OUT = ∠OTU = a (Base ∠s of 180 Δ)
∴ a + a + 70 = 180° (sum of ∠s of a Δ)
2a = 180° - 70°
2a = 110°
a = 55°
But ∠RUT + ∠RBT = 180° (opposite ∠s of a Cyclic quad)
∴ x + a = 100 = 180
x + 55 + 100 = 180
x = 180 - 155
x = 25
so ∠RUO = x = 25°