Math, asked by Mansitiwari544, 10 months ago

The number of sides of two regular polygon are in ratio 4:5and their interior angles are in ratio 15: 16 find the number of sides of polygon

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Answered by Anonymous

$\huge\star\underline\mathrm\blue{Answer:-}$ $<body bgcolor = lavender><marquee direction = "up"><font color = blue>$

If there are n sides

then interior angles =

$\frac{(n - 2) \times 180}{n}$

Let x and y are numbers of sides

$\frac{x}{y} = \frac{4}{5}$

interior angles =

$\frac{(x - 2) \times 180}{x}$

interior angles =

$\frac{( y- 2) \times 180}{y}$

$\frac{ \frac{(x - 2) \times 180}{x} }{ \frac{(y - 2) \times 180}{y} } = \frac{15}{16}$

$\frac{(x - 2) \times 180}{(y - 2) \times 180} \times \frac{y}{x} = \frac{15}{16}$

put x = 4y/5

$\frac{( \frac{4y}{5} - 2)}{(y - 2)} = \frac{3}{4}$

Answered by nidhirandhawa7

Step-by-step explanation:

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