In the diagram, \(\bar{YW}\) is a tangent to the circle at X, |UV| = |VX|...

Mathematics

WAEC 2016

In the diagram, \(\bar{YW}\) is a tangent to the circle at X, |UV| = |VX| and < VXW = 50º. Find the value of < UXY.

A. 70^o
B. 80^o
C. 105^o
D. 110^o

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Correct Answer: Option B

Explanation

In the diagram above, \(x_1\) = 50º(angles in alternate segment)

\(x_1\) = \(x_2\)(base angles of isos. \(\Delta\))

< UXY + \(x_2\) + 50º = 180º(sum of angles on a straight line)

< UXY + 50º + 50º = 180º

< UXY + 100º = 180º

< UXY = 180º - 100º

= 80º

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