How many sides does a polygon have if the sum of the measures of its angles is five times as large as the sum of the measures of its exterior angles?
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How many sides does a polygon have if the sum of the measures of its angles is five times as large as the sum of the measures of its exterior angles?
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Answer:
12 sides
Step-by-step explanation:
Number of sides is 12.
Sum of interior angle and exterior angle of a polygon is 180 degree.
Let exterior angle is x.
Interior angle is 5x.
x + 5x = 180°
x=30°
Sum of all exterior angles of a polygon is 360 degree
So n X x = 360°
n = 360°/30°
n=12