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2 years ago

Does anybody know? Find the value of x in the regular polygon

Mathematics

2 answers:

Gala2k [10]2 years ago

6 0

That is a dodecagon, so x without context is 150.

arlik [135]2 years ago

3 0

Answer:

x = 150

Step-by-step explanation:

The regular poligon shown in the image has 12 angles so it's a dodecagon

A dodecagon's interior angles is calculated with the following formula:

(n-2)180 (n is the count of angles)

10*180 = 1800 now this is the sum of all 12 angles' measure to find the value of x we divide this sum by 12

1800/12 = 150 this is the value of x

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Step-by-step explanation:

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${2}^{x + 2 } = 9 \times( {2}^{x} ) - 2\\\\2^x \cdot 2^2=9\cdot 2^x-2\\\\(9-4)2^x = 2\\\\2^x=\dfrac{2}{5}\\\\\text{We take the ln.}\\\\xln(2)=ln(2)-ln(5)\\\\x=\dfrac{ln(2)-ln(5)}{ln(2)}=-1.32193...$

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3 years ago