2005
Mathematics
67ca00ce0c643c71d77dee1f
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°THIS WEEK's
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