Part 1) What is the sum of the interior angle measures of a 20-gon?
we know that
The formula for getting the sum of interior angle is equal to
[tex]S=180*(n-2)[/tex]
where
S is the sum of the interior angles of a regular polygon.
n is the number of sides
In this problem we have
[tex]n=20\ sides[/tex]
substitute in the formula
[tex]S=180*(20-2)[/tex]
[tex]S=180*(18)=3,240\°[/tex]
therefore
the answer Part 1) is
the sum of the interior angle measures of a 20-gon is [tex]3,240\°[/tex]
Part 2) What is the measure of one interior angle of a regular 12-gon?
The formula for getting the sum of interior angle is equal to
[tex]S=180*(n-2)[/tex]
where
S is the sum of the interior angles of a regular polygon.
n is the number of sides
In this problem we have
[tex]n=12\ sides[/tex]
substitute in the formula
[tex]S=180*(12-2)[/tex]
[tex]S=180*(10)=1,800\°[/tex]
Divide the sum of the interior angles by the number of sides to obtain the measure of one interior angle
so
[tex]1,800\°/12=150\°[/tex]
therefore
the answer Part 2) is
the measure of one interior angle of a regular 12-gon is [tex]150\°[/tex]
Part 3) No diagram given
Part 4) What is the measure of an exterior angle of a regular octagon?
we know that
The sum of exterior angles of a regular polygon is equal to [tex]360[/tex] degrees
so
Divide the sum of exterior angles by the number of sides to obtain the measure of one exterior angle
the regular octagon has [tex]8[/tex] sides
[tex]360\°/8=45\°[/tex]
therefore
The answer Part 4) is
the measure of an exterior angle of a regular octagon is [tex]45\°[/tex]
Part 5) If the measure of an exterior angle of a regular polygon is 24, how many sides does the polygon have?
we know that
The sum of exterior angles of a regular polygon is equal to [tex]360[/tex] degrees
so
Divide the sum of exterior angles by the measure of an exterior angle to obtain the number of sides of the regular polygon
[tex]360\°/24\°=15\ sides[/tex]
therefore
the answer part 5) is
[tex]15\ sides[/tex]
