Answer:
Part a) The sum of the interior angle measures of a regular decagon is [tex]1,440\°[/tex]
Part b) The measure of each interior angle of a regular decagon is [tex]144\°[/tex]
Step-by-step explanation:
Part a)
we know that
The sum of the interior angles of a polygon is equal to
[tex]S=(n-2)180\°[/tex]
where
n is the number of sides of a polygon
In this problem
[tex]n=10[/tex] ----> regular decagon
substitute
[tex]S=(10-2)180\°=1,440\°[/tex]
Part b) What is the measure of each interior angle of a regular decagon?
If the figure is a regular polygon, then all interior angles are equal
so
Divide the sum of the interior angles by the number of sides
[tex]1,440\°/10=144\°[/tex]
