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lions [1.4K]
3 years ago
7

An interior angle of a regular polygon measures 170 degrees. How many sides does it have?

Mathematics
1 answer:
Leya [2.2K]3 years ago
7 0

\bf \textit{sum of all interior angles in a polygon}\\\\ n\theta =180(n-2)~~ \begin{cases} n= \stackrel{number~of}{sides}\\ \theta =\stackrel{angle~in}{degrees}\\[-0.5em] \hrulefill\\ \theta =170 \end{cases}\implies n170=180(n-2) \\\\\\ 170n=180n-360\implies 170n+360=180n\implies 360=10n \\\\\\ \cfrac{360}{10}=n\implies 36=n

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1 lapin a vu 6 éléphants en allant à la rivière. Chaque éléphant a vu 2 singes aller vers la rivière. Chaque singe tient 1 perro
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  • <u><em>31 animals</em></u>

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The question is in French language. The translation to English is:

<em>1 rabbit saw 6 elephants while going to the river. Each elephant saw 2 monkeys go towards the river. Each monkey holds 1 parrot in its hands.</em>

<em>How many animals are going to the river?</em>

<em />

<h2>Solution</h2>

<em />

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Elephants      6 (the rabbit saw 6 elephants)

Monkeys:       6 × 2 = 12 (2 monkeys per elephant)

Parrots:          12 × 1 = 12 (1 parrot per monkey)

                     =============================

Total:             1 + 6 + 12 + 12 = 31 animals ← answer

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