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3 years ago

Quadrilateral ABCD is inscribed in this circle.

Mathematics

1 answer:

otez555 [7]3 years ago

4 0

Answer:

107

Step-by-step explanation:

First note that this quadrilateral is cyclic.

One property of cyclic quadrilaterals is that opposite angles add up to 180.

since B and D are opposite angles, we can add them and set that to 180. we get that 5x+5=180, so x=35. Now, substituting 37 for x for all the angles, we get

A=73

B=66

D=114

To find C, notice that A and C are opposite angles. This means they add up to 180

73+C=180, C=107

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jeka94

Answer:

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Step-by-step explanation:

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3 years ago

What is the measure of arc WXY

bonufazy [111]

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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MrRa [10]

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2 years ago

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Elden [556K]

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Step-by-step explanation:

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3 0

3 years ago

​ Quadrilateral ABCD ​ is inscribed in this circle.

Quadrilateral ABCD is inscribed in this circle.