Question

Each interior angle of a regular polygon is four
times the exterior angle. Find the number of
sides in the polygon.​

Answer 1

Step-by-step explanation:

Interior angle + Exterior angle = 180 degrees

Let the exterior angle of the polygon is x and interior angle be 4×x = 4x

Now sum of Angles = 4x + x = 180 degrees

5x = 180 degrees

x = 180 degrees / 5 = 36 degrees

Exterior Angle = 36 degrees

Interior angle = 4× x = 4x = 36×4 = 144 degrees

Now n = 360/Ext. angle where n is the no. of sides

So, n = 360/36 = 10 sides

So the polygon has 10 sides

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Answer 2

$\rule{200}3$

$\tt\Large{\red{Question:-}}$

Each interior angle of a regular polygon is four

times the exterior angle. Find the number of

sides in the polygon.

$\tt\Large{\pink{Answer:-}}$

$\tt\large{\green{Given:-}}$

Each interior angle of a regular polygon is four

times the exterior angle.

$\tt\large{\blue{To\:find:-}}$

♦️Number of sides in the polygon?

$\tt\large{\green{Solution:-}}$

Every polygon has total 360 degrees in exterior when added.

So,

4 x 360=1440 degrees.

=>Let the number of sides be X

(X-2)x180=1440

(X-2)=1440/180=8

X=8+2=10

X = 10

$\rule{200}3$