The sum of angles of a polygon is 7200°. a) What is the sum of angles of polygon with one side less? b) What is the sum of angles of polygon with one side more?
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Answer:
Recall that the formula for the sum of the interior angles in a regular polygon is:
∣
∣
∣
∣
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
a
a
180
∘
(
n
−
2
)
a
a
∣
∣
−−−−−−−−−−−−−−−
where
−−−−−
:
n
=
number of sides
In your case, since the sum of the interior angles is
720
∘
, then the formula must equal to
720
∘
. Hence,
720
∘
=
180
∘
(
n
−
2
)
Since you are looking for
n
, the number of sides the polygon has, you must solve for
n
. Thus,
720
∘
180
∘
=
n
−
2
4
=
n
−
2
n
=
∣
∣
∣
∣
¯¯¯¯¯¯¯¯¯¯¯
a
a
6
a
a
∣
∣
−−−−−−
Since
n
=
6
, then the polygon has
6
side
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