A regular polygon has 40 sides . Find the measure of the interior and exterior angles
Answers
Step-by-step explanation:
A regular polygon with exterior angles of
40
o
would have 9 side and be a nonagon.
Explanation:
The exterior angles of any regular polygon must add up to
360
o
.
Since the angle measure given iin the questions s
40
o
, take
360
o
40
o
= 9. Meaning there are 9 exterior angles and therefore 9 sides to the polygon.
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A regular polygon refers to a multi-sided convex figure where all sides are equal in length and all angles have equal degree measures.
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The regular triangle has 3 interior angles of
60
o
and 3 exterior angles of
120
o
. The exterior angle have a sum of
360
o
=
(
3
)
120
o
The square has 4 interior angles of
90
o
and 4 exterior angles of
90
o
. The exterior angle have a sum of
360
o
=
(
4
)
90
o
.
The square has 5 interior angles of
108
o
and 5 exterior angles of
72
o
. The exterior angle have a sum of
360
o
=
(
5
)
72
o
.
In order to find the value of the interior angle of a regular polygon the equation is
(
n
−
2
)
180
n
where n is the number of sides of the regular polygon.
Triangle
(
3
−
2
)
180
3
=
60
o
Square
(
4
−
2
)
180
4
=
90
o
Pentagon
(
5
−
2
)
180
5
=
72
o
Finally
The interior and exterior angles of a regular polygon form a linear pair and therefore are supplementary and must add up to
180
o
.
Answer:
A regular polygon with an exterior angle measure of 40 degrees has nine sides. Every polygon's exterior angle sum equals 360. So 360/40 equals nine.
Step-by-step explanation: