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Question

For the given figure, find the angle XWU.


A
89o
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B
90o
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C
91o
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Solution

The correct option is C 91o
For the triangle UYZ,
Y+Z+U=180o
Y+59o+30o=180o
Y=180o59o30o=91o

We know that opposite angles of a cyclic quadrilateral have a sum of 180o.

For cyclic quadrilateral ZWXY,
Y+XWZ=180o
XWZ=180oY=180o91o
XWZ=89o

UWZ is a straight angle.
UWX+XWZ=180o
UWX=180oXWZ
UWX=180o89o=91o

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