Question

The ratio of the interior angle of a regular polygon to
its exterior angle is 4: 1. Find the number of sides of
the polygon.​

Answer 1

Answer:

Let the interior angle of the regular polygon be x.

Therefore, the exterior angle is x/4.

Exterior angle + adjacent interior angle = 180°

x/4 + x. = 180°

5x /4. = 180°

x. = 180° × 4/5

= 144°

The interior angle is 144°.

The exterior angle is 36°.

Let n be the number of sides.

n = 360°/ exterior angle

= 360° / 36°

= 10

The number of sides of a regular polygon is 10.

Answer 2

Answer:

10 sides

Step-by-step explanation:

The ratio of the interior angle of a regular polygon ro the exterior angle of the polygon=4:1

Total angle=4+1

=5

The exterior angle = 5x = 180

x=180/5

x=36

Let,n be the the number of sides

Then,n=360/exterior angle

=360/36

=10

Therefore,the no.of sides of the polygon=10