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Lines $XTQ$ and $XUR$ are tangent to a circle, as shown below.

If \(\angle ATQ = 41^\circ\) and \(\angle AUR = 63^\circ,\) then find \(\angle QXR,\) in degrees.

 Jun 12, 2020
 #1
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Lines \(XTQ\) and \(XUR\) are tangent to a circle, as shown below.

If \(\angle ATQ = 41^\circ\) and \(\angle AUR = 63^\circ\), then find \(\angle QXR\), in degrees.

 

\(\text{Let $\angle QXR = x $ }\)

\(\angle TCX = 360^\circ -2*90^\circ = 180^\circ - x\)

 

\(\begin{array}{|rcll|} \hline \mathbf{360^\circ} &=& \mathbf{(180^\circ - x)+82^\circ+126^\circ} \\ 360^\circ &=& 388^\circ - x \\ x &=& 388^\circ - 360^\circ \\ \mathbf{x} &=& \mathbf{28^\circ} \\ \hline \end{array}\)

 

The \(\angle QXR\) is \(\mathbf{28^\circ}\)

 

laugh

 Jun 12, 2020
edited by heureka  Jun 12, 2020

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