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makvit [3.9K]
3 years ago
7

What is the sum of the measure of the interior angles of a regular polygon if each exterior angle measures 72 degrees

Mathematics
2 answers:
valentina_108 [34]3 years ago
7 0

Answer: it’s 540°

Step-by-step explanation:

Pani-rosa [81]3 years ago
4 0
Sum of interior and exterior angle is 180 so

Interior angle =180−72=108

Now we need to find the no of sides of the polygon= n We know that interior angle of n-sides is given by

(n−2)×180n

We have

(n−2)×180=108n

or

180n−360=108n

or

72n=360

n=5 sides so there are 5 angles each of 108 degrees Sum of the interior angles=108+108+108+108+108=540.....
<span>To find the measure of each exterior angle of a regular polygon, you just divide 360 degrees by the number of sides. 
</span>
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