75.5k views
2 votes
The sum of the measures of the interior angles of a polygon is 5 times the sum of the measures of the exterior angles. How many sides does the polygon have

User Trisma
by
8.5k points

1 Answer

5 votes

Answer:

polygon has 12 sides

Explanation:

the sum of the exterior angles of a polygon is 360°

the sum of the interior angles of a polygon is

sum = 180° (n - 2 ) ← n is the number of sides

given the sum of the interior angles is 5 times sum of exterior angles, then

sum = 5 × 360° = 1800° then

180° (n - 2) = 1800 ( divide both sides by 180 )

n - 2 = 10 ( add 2 to both sides )

n = 12

Thus the polygon has 12 sides

User Kaspar
by
8.5k points

No related questions found