Find the number of sides of a polygon if the sum of the interior angles is 720
Answers
Explanation:
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
sides
Explanation:
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
sides