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

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

  • A.
    70o
  • B.
    80o
  • C.
    105o
  • D.
    110o
Correct Answer: Option B
Explanation

In the diagram above, x1 = 50(angles in alternate segment)
x1 = x2(base angles of isos. (Delta))
< UXY + x2 + 50o = 180o(sum of angles on a straight line)
< UXY + 50o + 50o = 180p
< UXY + 100o = 180o
< UXY = 180o – 100o
= 80o