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Dimas [21]
3 years ago
14

What is the measure of arc WXY

Mathematics
1 answer:
bonufazy [111]3 years ago
8 0

Answer:

152°

Step-by-step explanation:

Let P be any point on tangent \overleftrightarrow{YZ} and WY is secant or chord of the \odot J .

\therefore m\angle WYZ + m\angle WYP = 180°\\(Straight \: line \: \angle 's) \\\therefore 104° + m\angle WYP = 180°\\\therefore  m\angle WYP = 180°- 104° \\\red{\boxed {\bold {\therefore  m\angle WYP = 76°}}} \\

NOW, by tangent secant theorem:

m\angle WYP =\frac{1}{2}\times m(\widehat{WXY}) \\\\76°=\frac{1}{2}\times m( \widehat{WXY}) \\\\76°\times 2 =m( \widehat{WXY}) \\\huge \purple {\boxed {\therefore m(\widehat{WXY}) = 152°}}

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