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In the diagram,\angle U = 30, arc XY is 170, and arc VW is 110. Find arc WY, in degrees.

 Aug 11, 2020
 #1
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Arc WY - Arc XV = Angle U = 30 degrees.

 

Arc WY + Arx XV = 360 - 170 - 110 = 80 degrees.

 

Therefore, arc WY = (30 + 80)/2 = 55 degrees.

 Aug 11, 2020
 #2
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 Aug 12, 2020
 #3
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In the diagram, \(\angle U = 30^\circ\), arc XY is \(170^\circ\), and arc VW is \(110^\circ\).

Find arc WY, in degrees.

 

\(\begin{array}{|rcll|} \hline \mathbf{\text{ In $\triangle $ UWY}} \\ \hline \mathbf{180^\circ} &=& \mathbf{U + \left(90^\circ-\dfrac{170^\circ}{2}+ 90^\circ-\dfrac{WY}{2}\right)} \\ && \quad \mathbf{ +\left(90^\circ-\dfrac{110^\circ}{2}+ 90^\circ-\dfrac{WY}{2} \right)} \\\\ 180^\circ &=& U + \left(180^\circ-85^\circ-\dfrac{WY}{2}\right) \\ && \quad + \left(180^\circ-55^\circ-\dfrac{WY}{2} \right) \\\\ 180^\circ &=& U + 95^\circ-\dfrac{WY}{2} + 125^\circ-\dfrac{WY}{2} \\\\ 180^\circ &=& U + 220^\circ - WY \quad | \quad U=30^\circ \\ 180^\circ &=& 30^\circ + 220^\circ - WY \\ 180^\circ &=& 250^\circ - WY \\ WY &=& 250^\circ - 180^\circ \\ \mathbf{WY} &=& \mathbf{70^\circ} \\ \hline \end{array}\)

 

laugh

 Aug 12, 2020

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