0
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: .
Add your answer:
Earn +20 pts
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
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.
What are the interior angles of a polygon?
They are angles between adjacent sides of the polygon, measured on the inside of the shape.
How do you find the sum of all the angles inside a regular polygon?
Count the number of sides = N. Then sum of all the interior angles = (N -2)*180 degrees.
What is the total interior angle of a regular polygon if 20 triangles can be drawn inside the polygon?
20 triangles will fit into a 22 sided polygon whose interior angles add up to 3600 degrees
How many triangles does a 1002 sided polygon have?
Any n-sided polygon (n being any integer) will always have a minimum of n-2 triangles inside the shape, assuming that the polygon is regular with no reflex angles.
What is the difference between a regular polygon and a concave polygon?
A regular polygon has all its sides equal and all its angles equal. One consequence is that no angle can be reflex (between 180 and 360 degrees). A concave polygon, on the other hand, must have at least one angle that is a reflex angle. The line joining any two points inside any convex polygon (and that includes regular ones) must lie wholly within the polygon. In a concave polygon, it must be possible to find two point inside the polygon such that the line joining them crosses the boundaries of the polygon.
What is the attribute of the hexagon?
It is a 6 sided polygon It has 6 inside angles that add up to 720 degrees It can be a regular or an irregular hexagon It will tessellate as a regular hexagon It has 9 diagonals It has 6 outside angles that add up to 360 degrees
What is the rule for the sum of angles inside of a polygon?
It is: ('n'-2)*180 = sum of interior angles whereas 'n' is the number of sides of the polygon
Is there a rule for the sum of angles inside a polygon?
Yes and it is: ('n'-2)*180 = sum of interior angles whereas 'n' is the number of sides of the polygon
What is the name of that angles that form by a side of a polygon and and adjacent side?
If measured on the inside of the polygon, the it is an interior angle.
What does adjacent interior angles mean in math?
It means two angles inside a polygon that share a side.
A Polygon whose vertices are on a circle and whose other points are inside the circle?
Inscribed Polygon
