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By drawing all the diagonals from one vertex, the polygon is divided up into triangles. The sum of the interior angles of the polygon is equal to the sum of the internal angles in the triangles.
With n vertices, each vertex is not directly connected to n-3 other vertices, thus n-3 diagonals can be drawn from a vertex which will create n-2 triangles (each with the sum of their interior angles as 180o); so:
sum_of_interior_angles = 180 x (number_of_sides - 2)
What else can I help you with?
How can you determine the sum of the exterior angles of a given polygon?
You can do it by memorizing this statement:" The sum of the exterior angles of every polygon is 360 degrees. "
What is the sum of interior angles of a icosagon?
That will depend on what type of isogon it is because an isogon is the name given to any regular polygon whose interior angles are equal.But in the general: (n-2)*180 = sum of interior of any polygon whereas 'n' is the number of sides of the polygon.
Sum of angles of a nonagon?
The sum of the interior angles of a nonagon is 1260 degrees. A nonagon is a nine-sided polygon in geometry. The formula to find the sum of interior angles in a polygon is given by the formula [n-2] x 180 degrees, where n represents the number of sides.
Given an interior angle how do you find the sum of exterior angles of a polygon?
Given a shape as such... ______________________________________ / A=72 B=65 \ \ / \_C=105__________________D=110_______/ (sorta) You take the interior angles that you have and subtract them from 360 to get their supplementary angles, which would be the measure of the outside angles corresponding to the interior angles Measure of <A= 72- so 360- 72=288*; so the measure of the exterior angle corresponding to <A is 288* You can do the same thing for the rest of the angles in the polygon. Hope it helps...
What is the sum of the interior angle measures of a 40- sided convex polygon?
The sum of the interior angles of a convex polygon with n sides is given by (n-2)x180o. So for a 40 sided polygon n=40; thus (40-2)x180o = 38x180o = 6840o.
What is sum of the interior angles of a polygon with three sides?
the sum of the interior angles of a 3 sided polygon is = 180 degrees. the sum of the interior angles of any polygon is given by 540/n. in this case n is = 3
What polygons interior angles equal 8640 degrees?
A polygon with 50 sides, given the sum of all the interior angles in 8640.
How can you determine the sum of the exterior angles of a given polygon?
You can do it by memorizing this statement:" The sum of the exterior angles of every polygon is 360 degrees. "
What is the sum of interior angles of a icosagon?
That will depend on what type of isogon it is because an isogon is the name given to any regular polygon whose interior angles are equal.But in the general: (n-2)*180 = sum of interior of any polygon whereas 'n' is the number of sides of the polygon.
What is the sum of the interior angles if the exterior angles are 24?
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 = 15For 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, andinterior_angle + exterior_angle = 180°→ exterior_angle = 180° - interior_angle→ exterior_angle = 180° - 156° = 24° (as given in the question).
What is the relationship between interior angles and the sum of the exterior angles of a given polygon?
There isn't one. The sum of the exterior angles is always 360 degrees, the sum of the interior angles varies depending on the number of sides.
How do you determine the number of angles of a polygon given the number of sides?
The two numbers are the same.
What is the rule for finding out the sum interior angle of a polygon?
To find the sum of the interior angles and the sum of the exterior angles of any polygon. To review linear measurement to the nearest sixteenth of an inch and angle measurement to the nearest degree. To construct a polygon and its exterior angles given the number of sides. hope this helped
One exterior angle of a regular polygon measures 40 What is the sum of the polygon's interior angle measures?
The sum of a regular polygon's interior angles is always equal to (n-2) * 180, where n is the number of sides in the polygon. Given that one exterior angle measures 40 degrees, we can find the interior angle by subtracting 40 from 180 degrees (since the exterior and interior angles are supplementary) to get 140 degrees. So, the sum of the interior angles of the regular polygon is 140 * n.
Sum of angles of a nonagon?
The sum of the interior angles of a nonagon is 1260 degrees. A nonagon is a nine-sided polygon in geometry. The formula to find the sum of interior angles in a polygon is given by the formula [n-2] x 180 degrees, where n represents the number of sides.
Given an interior angle how do you find the sum of exterior angles of a polygon?
Given a shape as such... ______________________________________ / A=72 B=65 \ \ / \_C=105__________________D=110_______/ (sorta) You take the interior angles that you have and subtract them from 360 to get their supplementary angles, which would be the measure of the outside angles corresponding to the interior angles Measure of <A= 72- so 360- 72=288*; so the measure of the exterior angle corresponding to <A is 288* You can do the same thing for the rest of the angles in the polygon. Hope it helps...
How do you find the number of sides in an equiangular polygon given the measures of the interior angles?
Type your answer here... The sum of the angles in all polygons is 360 degrees. Thus, if you know the measure of the interior angles you can divide 360 by the measurement to find out how many interior angles and sides there are.
