In the diagram, \(\bar{YW}\) is a tangent to the circle at X, |UV| = |VX| and < VXW = 50º. Find the value of < UXY.
Attached Figure / Diagram
A
70o
B
80o
C
105o
D
110o
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #46153)