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What is the sum of the interior angles if the exterior angles are 24?
Wiki User
∙ 8y ago
The sum of the exterior angles is 360°; for a regular polygon this gives:
sum_exterior_angles = number_of_sides × exterior_angle = 360°
→ number_of_sides = 360° ÷ exterior_angle = 15
For any polygon, the sum of the interior angles is given by:
sum_interior_angles = (number_of_sides - 2) × 180°
→ sum_interior_angles = (15 - 2) × 180°
→ sum_interior_angles = 13 × 180° = 2340°
This can be checked since: 2340° ÷ 15 = 156° for the interior angle of a regular 15 sided polygon, and
interior_angle + exterior_angle = 180°
→ exterior_angle = 180° - interior_angle
→ exterior_angle = 180° - 156° = 24° (as given in the question).
Wiki User
∙ 8y ago
The sum of the interior angles of any polygon is equal to (n-2) * 180 degrees, where n is the number of sides of the polygon. Since the exterior angles of a polygon are supplementary to the interior angles, if the exterior angles are 24 degrees, the interior angles would be 180 - 24 = 156 degrees.
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What is the interior and exterior angles for a 24 sided shape?
Any value you like, between 0 and 360 degrees, other than 180 degrees. Any oair of interior and exterior angles must sum to 180 degrees.
What is the sum of the interior angle measures of a 15 sided polygon?
Remember Exterior angle = 360 / No. of sides. Hence Exterior Angle = 360//25 = 24 degrees, It follows that the intertiot angle is 180 - 24 =156 degrees. There are 15 interior angles Hence 15 x 156 = 2340 degrees is the sum of the interior angles of a 'Pentadecagon'.
What is the measure of 1 angle of a regular 24-gon?
Exterior angle is 360/24 ie 15o so interior angle is 180 - 15 ie 165o. Another method is to use the formula "(2n - 4) right angles", which is the sum of the interior angles of an n-sided polygon. In this case n = 24 so total of the interior angles is (48 - 4) x 90 which is 3960o. Dividing this by the number of interior angles, 24, also gives 165o.
What is the sum of the interior angles of 24-gon?
It is: (24-2)*180 = 3960 degrees
What is the angle sum of the interior angles if the exterior angle is 24 and interior angle is 15?
A exterior angle of 24 and an interior angle of 15 is not a credible combination. There needs to be a lot more information before an answer can be attempted.A exterior angle of 24 and an interior angle of 15 is not a credible combination. There needs to be a lot more information before an answer can be attempted.A exterior angle of 24 and an interior angle of 15 is not a credible combination. There needs to be a lot more information before an answer can be attempted.A exterior angle of 24 and an interior angle of 15 is not a credible combination. There needs to be a lot more information before an answer can be attempted.
What is the sum of angles in a 24 sided polygon?
Exterior angles: 360 degrees Interior angles: 3,960 degrees
What polygon has a sum of exterior angles which is 15 times its interior angle sums?
There can be no such polygon. The sum of exterior angles of any polygon is 360 degrees. If the sum of the exterior angles is 15 times the sum of the interior angles, then the sum of the interior angles must be 360/15 = 24 degrees. Now, the sum of the interior angles of a polygon with n sides is (n-2)*180 degrees So (n-2)*180 = 24 That is, (n-2) = 24/180 = 0.133... and so n = 2.133...sides But n must be an integer and it must be greater than or equal to 3.
What is the sum of the measures of the exterior and interior angles of a convex 24-gon?
The sum of the exterior angles of any convex polygon is always 360 degrees. The sum of the interior angles of any convex n-gon is (n-2) * 180 degrees, because any convex n-gon can be represented as n-2 triangles, and the sum of the interior angles of a triangle is 180 degrees.
What is the sum of an interior angle measure of a 15-gon?
Assuming that this is a regular pentadecagon, the 360° of the exterior offset angles are spread evenly, so are 24° each. This means the interior angles are 180-24=156°
What is the interior and exterior angles for a 24 sided shape?
Any value you like, between 0 and 360 degrees, other than 180 degrees. Any oair of interior and exterior angles must sum to 180 degrees.
What is the interior and exterior angles of a 24- gon?
Interior angles add up to 3960 degrees Exterior angles add up to 360 degrees
What tdo the interior and exterior angles of a 24 sided polygon add up to?
Interior angles using the formula: (24-2)*180 = 3960 degrees Exterior angles: 360 degrees
What are the sum of the exterior angles of a 24- gon?
360 degrees
What are the sum of the interior angles of a 24-gon?
The interior angles add up to 3960 degrees
What is the sum of the interior angles of a 24-gon?
4,320
How do you find the measure of an interior and exterior angle of a 15-gon?
Example: a regular 15-gon The sum of the interior angles of any regular polygon of n sides is equal to 180(n - 2) degrees. 180 x 13 = 2340 There are fifteen angles. 2340/15 = 156 An interior angle of a regular 15-gon is 156 degrees. There are two ways to find the exterior angles. The interior and exterior angles add up to 180. 180 - 156 = 24. The exterior angles of any polygon add up to 360. 360/15 = 24
What is the sum of the exterior angles in a 24 sided shape?
360 degrees is.
