Answer: [tex]144\°[/tex]
Step-by-step explanation:
Regular polygons are those polygons whose sides are equal in length and whose angles are all equal.
By definition each interior angle of a Regular polygon is given by:
[tex]\frac{180 ( n -2 )}{n}[/tex] (In degrees)
Where "n" is the number of sides of the polygon.
In this case you know that the polygon shown in the picture is a Decagon, which means that it has 10 sides. Then:
[tex]n=10[/tex]
Therefore, you must substitute that value of "n" into [tex]\frac{180 ( n -2 )}{n}[/tex] and then you must evaluate.
Through this procedure, you get that the measure of an interior angle of the Regular Decagon is:
[tex]\frac{180 ( 10 -2)}{10}=\frac{180 (8 )}{10}=\frac{1440}{10}=144\°[/tex]
