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aleksandrvk [35]
3 years ago
7

The measure of each interior angle of a regular 100-gon is (3x + 26.4).What is the value of x?​

Mathematics
1 answer:
Sonbull [250]3 years ago
5 0

\bf \textit{sum of all interior angles in a polygon}\\\\ n\theta = 180(n-2)~~ \begin{cases} n = sides\\ \theta =angle~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ n= 100 \end{cases}\implies \theta 100=180(100-2) \\\\\\ 100\theta = 180(98)\implies 100\theta =17640\implies \theta =\cfrac{17640}{100}\implies \theta = \cfrac{882}{5}

which is pretty much just 176.4°, well, we also know that θ = 3x + 26.4

\bf 176.4 = 3x + 26.4\implies 150 = 3x\implies \cfrac{150}{3}=x\implies 50=x

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ArbitrLikvidat [17]

Answer:

t=57, u=31, v=92

Step-by-step explanation:

So we know that 180= 5x+2+2x+9+8x+4 which simplifies to 180 = 15x+15. Subtract 15 from both sides to get 165=15x and then divide by 15 to get 11=x. NOw we can plug this into the three angles as x so t = 5*11+2, t=55+2, t=57, then u = 2*11+9, u=22+9, u=31, and lastly v=8*11+4, v= 88+4, and v=92

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Answer:

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Step-by-step explanation:

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Hope I helped!

Best regards!!

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Stepby-step explanation:

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