Question

the ratio of an interior angle to exterior angle of regular polygon is 5:1 find number of sides​

Answer 1

Answer:

$\huge{\textbf{\textsf{{\color{navy}{Sol}}{\purple{uti}}{\pink{on}}{\color{pink}{:}}}}}$

GIVEN :-

• the ratio of an interior angle to exterior angle of regular polygon is 5:1

RTF :-

• number of sides

SOLUTION :-

let's take interrior and exterior angle as 5x and 1x

we know the the sum of exterior and interior angle is 180°

so, 5x + x = 180°

6x = 180°

x = $\frac{180}{6}$

x = 30°

now interrior angle = 5x = 5×30° = 150°

exterior angle = x = 30°

NOW SIDES OF POLYGON

to find sides first we have to subtract interrior angle from 180° and divide by 360°

= 180° - 150°

= 30°

now divide with 360°

= $\frac{360°}{30}$

= 6 sides

therefore, this polygon have 6 sides

Answer 2

MARK UPPER ONE BRAINLIEST$\huge\color{red}!!!!!!!!!!!$

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GIVEN :-

• the ratio of an interior angle to exterior angle of regular polygon is 5:1

RTF :-

• number of sides

SOLUTION :-

let's take interrior and exterior angle as 5x and 1x

we know the the sum of exterior and interior angle is 180°

so, 5x + x = 180°

6x = 180°

x = $\frac{180}{6}$

6

180

x = 30°

now interrior angle = 5x = 5×30° = 150°

exterior angle = x = 30°

NOW SIDES OF POLYGON

to find sides first we have to subtract interrior angle from 180° and divide by 360°

= 180° - 150°

= 30°

now divide with 360°

= $\frac{360°}{30}$

30

360°

= 6 sides

therefore, this polygon have 6 sides