Answer:
Part a) The measure of the sum of all angles in a regular dodecagon is equal to 1,800 degrees
Part b) The measure of one of its interiors angles is 150 degrees
Part c) The measure of one of its exterior angles is 30 degrees
Step-by-step explanation:
Part a) What is the measure of the sum of all angles in a regular dodecagon (12 sides)
we know that
The formula to calculate the sum of the interior angles in a regular polygon is equal to
[tex]S=(n-2)180^o[/tex]
where
n is the number of sides of regular polygon
In this problem a regular dodecagon has n=12 sides
substitute
[tex]S=(12-2)180^o[/tex]
[tex]S=(10)180^o[/tex]
[tex]S=1,800^o[/tex]
Part b) What is the measure of one of its interiors angles?
To find out the measure of one of its interior angles, divide the sum of all angles by the number of sides
[tex]1,800^o/12=150^o[/tex]
Part c) What is the measure of one of its exterior angles?
we know that
The sum of one interior angle and its corresponding exterior angle must be equal to 180 degrees
Let
x ---> the measure of one exterior angle
[tex]150^o+x=180^o[/tex]
solve for x
[tex]x=180^o-150^o[/tex]
[tex]x=30^o[/tex]
