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3 years ago

Find the measure of each interior angle of the regular polygon

Mathematics

1 answer:

lukranit [14]3 years ago

5 0

Answer:

140 deg

Step-by-step explanation:

The sum of the measures of the interior angles of an n-gon is

(n - 2)180

In a 9-gon, there are 9 sides, so n = 9.

The sum of the measures of the interior angles of a 9-gon is

(n - 2)180 =

= (9 - 2)(180)

= 7(180)

= 1260

A regular polygon has congruent interior angles. A 9-gon has 9 congruent interior angles. The measure of each interior angle is the sum of the measures of the interior angles divided by the number of angles.

1260/9 = 140

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4/5 divided by 1/3 plus 1/5 minus 3/5

r-ruslan [8.4K]

Answer:

$\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}=-12$

Step-by-step explanation:

Considering the expression

$\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}$

Solution Steps:

$\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}$

$\mathrm{Combine\:the\:fractions\:}\frac{1}{5}-\frac{3}{5}:\quad -\frac{2}{5}$

$=\frac{\frac{4}{5}}{\frac{1}{3}-\frac{2}{5}}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{b}{c}}{a}=\frac{b}{c\:\cdot \:a}$

$=\frac{4}{5\left(\frac{1}{3}-\frac{2}{5}\right)}$

join $\frac{1}{3}-\frac{2}{5}:\quad -\frac{1}{15}$

$=\frac{4}{5\left(-\frac{1}{15}\right)}$

$\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a$

$=\frac{4}{-5\cdot \frac{1}{15}}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}$

$=-\frac{4}{5\cdot \frac{1}{15}}$

$\mathrm{Multiply\:}5\cdot \frac{1}{15}\::\quad \frac{1}{3}$

$=-\frac{4}{\frac{1}{3}}$

$\mathrm{Simplify}\:\frac{4}{\frac{1}{3}}:\quad \frac{12}{1}$

$=-\frac{12}{1}$

$\mathrm{Apply\:rule}\:\frac{a}{1}=a$

$=-12$

Therefore

$\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}=-12$

4 0

3 years ago

Find the measure of each interior angle of the regular polygon​

Find the measure of each interior angle of the regular polygon