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What is the sum of the interior angles of a regular polygon if each exterior angle measures 72?
Wiki User
∙ 11y ago
The sum of the exterior angles of a polygon is 360o
If the exterior angle of a regular polygon is 72o, then:
number_of_sides x 72o = 360o
⇒ number_of_sides = 360o ÷ 72o
= 5 sides
total_of_interior_angles = (number_of_sides - 2) x 180o
= (5 - 2 ) x 180o
= 540o
Alternatively for the second half once the number of sides is known:
interior_angle = 180o - exterior_angle
= 180o - 72o
= 108o
total_of_interior_angles = number_of_sides x interior_angle
= 5 x 108o
= 540o
Wiki User
∙ 11y ago
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One exterior angle of a regular polygon measures 36 What is the sum of the polygon's interior angle measures?
1440 degrees
One exterior angle of a regular polygon measures 36. What is the sum of the polygon's interior angle measures?
1440 degrees
One exterior angle of a regular polygon measures 30 degrees what is the sum of the polygon's interior angle measures?
1800 degrees
What is the sum of the measures of the interior angles of a regular polygon if each exterior angle measures 90?
360
What is the sum of the measures of the interior angles of a regular of a regular polygon if each exterior angle measures 120?
If exterior angles are 120 then interior angles must be 60 so you have an equilateral triangle
What is the sum of the measures of the interior angles of the regular polygon if each exterior measures 120?
Hint: in a regular polygon interior plus exterior = 180o, always.
One exterior angle of a regular polygon measures 40 What is the sum of the polygon's interior angle measures?
1260
What is the sum of the measures of the interior of a regular polygon if each exterior angle measures 90?
360
One exterior angle of a regular polygon measures 36 What is the sum of the polygon's interior angle measures?
1440 degrees
One exterior angle of a regular polygon measures 36. What is the sum of the polygon's interior angle measures?
1440 degrees
One exterior angle of a regular polygon measures 30 degrees what is the sum of the polygon's interior angle measures?
1800 degrees
What is the sum of the measures of the interior angles of a regular polygon if each exterior angle measures 90?
360
What is the sum of the measures of the interior angles of a regular of a regular polygon if each exterior angle measures 120?
If exterior angles are 120 then interior angles must be 60 so you have an equilateral triangle
What is the measures of the interior angles of a regular polygon if each exterior angle measures 72?
The interior angle of any regular polygon can be calculated using the formula 180 * (n - 2) / n, where n is the number of sides. In this case, since each exterior angle measures 72 degrees, the interior angle would be 180 - 72 = 108 degrees. So the measures of the interior angles in this regular polygon would be 108 degrees.
What is the sum of the polygon's interior angle measures if the exterior angle of a regular polygon's 36 degree?
1440 degrees
What is the sum of the measures of the interior angles of a regular polygon if each exterior angle measures 72?
540 degrees
What is the measures of an interior angle and an exterior angle of a regular polygon with 6 sides?
Interior angle = 120 degrees Exterior angle = 60 degrees
