Polygon Angle Sum Theorem Worksheet

📆 Updated: 1 Jan 1970
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Are you a math teacher searching for a comprehensive worksheet on the Polygon Angle Sum Theorem? Look no further. This worksheet is designed to help high school geometry students solidify their understanding of this fundamental concept.



Table of Images 👆

  1. Triangle Angle Sum Theorem Worksheet
  2. Interior Angles of Regular Polygons Worksheet
  3. Triangle Properties Worksheet
  4. Regular Polygon Definition
Triangle Angle Sum Theorem Worksheet
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Interior Angles of Regular Polygons Worksheet
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Triangle Properties Worksheet
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Regular Polygon Definition
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Regular Polygon Definition
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Regular Polygon Definition
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Regular Polygon Definition
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Regular Polygon Definition
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Regular Polygon Definition
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Regular Polygon Definition
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Regular Polygon Definition
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Regular Polygon Definition
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Regular Polygon Definition
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Regular Polygon Definition
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Regular Polygon Definition
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Regular Polygon Definition
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Regular Polygon Definition
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Regular Polygon Definition
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State the polygon angle sum theorem.

The polygon angle sum theorem states that the sum of the interior angles of a polygon with n sides is equal to (n-2) multiplied by 180 degrees.

How many sides does a polygon with an angle sum of 180 degrees have?

A polygon with an angle sum of 180 degrees has 3 sides, and it is known as a triangle.

What is the angle sum of a triangle?

The angle sum of a triangle is always 180 degrees. This fundamental property of triangles is known as the Triangle Angle Sum Theorem, which states that the sum of the interior angles of a triangle is always equal to 180 degrees. This theorem applies to all types of triangles, whether they are equilateral, isosceles, or scalene.

Can a polygon have an angle sum greater than 180 degrees? Why or why not?

No, a polygon cannot have an angle sum greater than 180 degrees. The sum of the interior angles of a polygon is always equal to (n-2) * 180 degrees, where n is the number of sides. Since any polygon must have at least 3 sides (triangle), the minimum sum of the interior angles would be 180 degrees (3-2*180 = 180). Therefore, it is not possible for a polygon to have an angle sum greater than 180 degrees based on the formula for calculating the interior angles of a polygon.

What is the angle sum of a quadrilateral?

The angle sum of a quadrilateral is 360 degrees.

How many angles does a pentagon have?

A pentagon has five angles.

What is the angle sum of a hexagon?

The angle sum of a hexagon is 720 degrees.

Can a polygon have an angle sum less than 360 degrees? Why or why not?

No, a polygon cannot have an angle sum less than 360 degrees. This is because the sum of the interior angles of any polygon is always equal to 180 degrees less than the number of sides multiplied by 180 degrees. Since the minimum number of sides for a polygon is 3 (a triangle), the minimum angle sum would be 180 degrees (3 sides - 2) x 180 degrees = 180 degrees. Thus, a polygon must have an angle sum equal to or greater than 360 degrees.

How many sides does an octagon have if its angle sum is 1080 degrees?

An octagon has 8 sides, as each interior angle of an octagon measures 135 degrees, so the sum of all interior angles in an octagon is 1080 degrees.

Is it possible for a polygon to have two different angle sums? Why or why not?

No, it is not possible for a polygon to have two different angle sums. The sum of the interior angles of a polygon is always constant and can be calculated using the formula (n-2) * 180 degrees, where n represents the number of sides. This means that the angle sum of a polygon is uniquely determined by the number of sides it has, and cannot have two different values.

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