Find the number of sides in a regular
polygon, its interior angle is equal to its
exterior angle
Answers
Answered by
3
Step-by-step explanation:
The sum of exterior angle and its adjacent interior is 180
0
, that is,
e+i=180
0
Since each exterior angle is equal to one third its adjacent interior angle, therefore, substitute
3
i
=e or i=3e.
e+3e=180
0
⇒4e=180
0
⇒e=
4
180
0
=45
0
We know that the measure of exterior angle is e=(
n
360
)
0
where n is the number of sides.
Here, it is given that the exterior angle is e=45
0
, therefore,
n=
e
360
=
45
360
=8
Hence, the number of sides is 8.
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