If each interior angle of a regular polygon is x^o and each exterior angle is

If each interior angle of a regular polygon is $x^o$and each exterior angle is
$\frac{x - 36}{3}$
Calculate the sum of the interior angles in the polygon.

Answers

Interior angle + exterior angles = $180^o$

$\frac{x-36}{3}$ + x = 180

$\frac{x-36+3x}{3}$ = 180

4x - 36 = 540;

4x = 576

x = 144

Exterior angle

= $\frac{144-36}{3}$ = $\frac{108}{3}$ = $36^o$

the number of sides = $\frac{360}{36}$ = 10

Sum of interior angle is

= (2n - 4)90 = (2 x 10 - 4)90

= (20 - 4)90 = 16 x 90 = $1440^o$

x = 144

Exterior angle

= $\frac{144-36}{3}$ = $\frac{108}{3}$ = $36^o$

the number of sides = $\frac{360}{36}$ = 10

Sum of interior angles is

= (2n - 4)90 = (2 x 10 - 4)90

= (20 - 4)$90^o$ = 16

johnmulu answered the question on June 10, 2017 at 06:22

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