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

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

70^o

80^o

105^o

110^o

Correct answer is B

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

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

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