Question

I need help please and thank you

Answer 1

Answer: $144\°$

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:

$\frac{180 ( n -2 )}{n}$  (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:

$n=10$

Therefore, you must substitute that value of "n" into  $\frac{180 ( n -2 )}{n}$   and then you must evaluate.

Through this procedure, you get that the measure of an interior angle of the Regular Decagon is:

$\frac{180 ( 10 -2)}{10}=\frac{180 (8 )}{10}=\frac{1440}{10}=144\°$