How much is one outer angle for a 24 sided regular polygon? How much is its one inner angle ? What is the sum of the inner angles ? very arregent please sent the answer
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The formula for the sum of the interior angles of a polygon is
(
n
−
2
)
⋅
180
, where
n
is the number of sides.
For a
24
-gon,
n
=
24
.
(
24
−
2
)
⋅
180
=
3960
.
Another method is to use exterior angles. An
n
-gon has
n
exterior angles.
An exterior angles measures
360
n
.
An interior angle equals
180
minus the exterior angle.
A
24
-gon has
24
exterior angles.
Each exterior angle measures
360
24
=
15
.
The interior angle measures
180
−
15
=
165
.
The sum of the
24
interior angles is then
24
⋅
165
=
3960
.
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