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Novosadov [1.4K]
3 years ago
14

What is the sum of the measures of interior angles ofna regular polygon if each exterior angle measures 72°?

Mathematics
1 answer:
WARRIOR [948]3 years ago
5 0
We know that

The exterior angle measures of a polygon must add up to 360°, 

therefore

 360°/72°=5 exterior angles

so

5 exterior angles, would mean 5 interior angles and therefore  5 sides to the polygon

The exterior angle and the interior angle of any polygon are supplementary and must add up to 180°.

exterior angle+interior angle=180°

interior angle=180°-exterior angle

interior angle=180°−72°-------> 108°
Each interior angle is 108°

The sum of the interior angles would be 

5*108°=540°

the answer is

540°

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