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Theorem: The sum of the interior angles in a polygon with n sides is 180º(n - 2).In the pentagon below, we have labeled the interior angles 1, 2, 3, 4, and 5. Each of these is supplementary respectively to exterior angles 6, 7, 8, 9, and 10. Therefore we have: We know that angles 1 through 5 in a pentagon have a sum of 540º. We substitute 540º for these angles and we have:. Subtracting 540º from both sides, we can find the sum of the five exterior angles of this pentagon: .
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What are the interior and exterior angles in a regular polygon?
A polygon is a closed figure in the plane. It has an inside and an outside.The angles on the inside are the interior angles. An exterior angle is the angle between any side of the polygon and a line extended from the next side.Here is an example to help.If you draw an triangle, the angles inside it are interior angles. Then if you extend any side, the angle between that line and the next side is the exterior angle.The sum of the exteriors is always 360. For a polygon with n sides, the sum of the interior angles is 180 (n-2) degrees.
A Polygon whose vertices are on a circle and whose other points are inside the circle?
Inscribed Polygon
What is the interior angle of a pentagon?
The measurement of an interior angle of a pentagon depends on whether the pentagon is a "regular pentagon". The sum of the measures of the interior angles of any polygon can be calculated using the formula (n-2)180, where n = the number of sides. If the pentagon is a regular pentagon, then all of the interior angles are congruent (i.e. : 144 degrees). Interior angle is the inside angle of any angular object. A triangle for instance has three outside angles and three interior angles, the angles of the points from the inside.
What is the sum of the interior angle of a 13-sided polygon?
The sum of the interior angles of a triangle is 180 deg. For a convex polygon with n sides we can divide it to n-2 triangles. So the answer, if the polygon is convex, is (13-2)*180= 1980 deg * * * * * The polygon need not be convex. The formula for the sum of the interior angles is valid as long as the polygon is simple - that it, its sides do not cross each other inside the polygon.
Are the angles inside a regular octagon or acute or obtuse?
acute
