Question

The exterior and interior angles of a regular polygon are in the ratio 1:9. Find i) a number of sides of the polygon ii) sum of all interior angles of the polygon. Class 8 Chapter 4

Answer 1

Answer:

ANSWER

The ratio between the interior angle and the exterior angle of a regular polygon is 2:1.

Each interior angle of a regular polygon =

n

180

o

(n−2)

where n= number of sides of polygon

Each exterior angle of a regular polygon =

n

360

o

According to question,

n

180

o

(n−2)

:

n

360

o

=2:1

=>

2

(n−2)

=

1

2

=>n−2=4

=>n=6

Number of sides of the polygon =6

Step-by-step explanation:

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