Question

What is the measure of arc WXY

Answer 1

152°

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) \\</p><p>\therefore 104° + m\angle WYP = 180°\\</p><p>\therefore m\angle WYP = 180°- 104° \\</p><p>\red{\boxed {\bold {\therefore m\angle WYP = 76°}}} \\`

NOW, by tangent secant theorem:

`m\angle WYP =(1)/(2)* m(\widehat{WXY}) \\\\</p><p>76°=(1)/(2)* m( \widehat{WXY}) \\\\</p><p>76°* 2 =m( \widehat{WXY}) \\</p><p>\huge \purple {\boxed {\therefore m(\widehat{WXY}) = 152°}}`