"Sum of interior angles and sum of exterior angles of polygons" PPT courseware

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"Sum of interior angles and sum of exterior angles of polygons" PPT courseware

Part I: Polygons

In a plane, a closed figure composed of several line segments that are not on the same straight line connected end to end is called a polygon.

Diagonal: In a polygon, the line segment connecting two non-adjacent vertices is called the diagonal of the polygon.

Exterior angle: The angle formed by one side of a polygon and the reverse extension of the other side is called the exterior angle of the polygon.

1. What is the sum of the interior angles of the triangle?

∠1+∠2+∠3=? 180°

2. What is the sum of the interior angles of the quadrilateral?

3. What is the sum of the interior angles of the pentagon?

4. What is the sum of the interior angles of a hexagon?

5. What is the sum of the interior angles of an n-sided polygon?

The sum of the interior angles and the sum of the exterior angles of a polygon PPT, Part 2 content: The sum of the interior angles of a polygon

The sum of the interior angles of an n-sided polygon is (n-2) × 180°

Example: Find the measure of the sum of the interior angles of a 15-sided polygon.

Solution: (n-2)×180°

=(15-2)×180°

= 2340°

Answer: The sum of the interior angles of a 15-sided polygon is 2340°

Consolidation exercise one:

1. The sum of the interior angles of a heptagon is ( )

2. The sum of the interior angles of a decagon is ( )

3. The sum of the interior angles of a seventeen-sided polygon is ( )

4. The sum of the interior angles of an icosagon is ( )

5. The sum of the interior angles of an octagon is ( )

The sum of the interior angles and the sum of the exterior angles of a polygon PPT, Part 3: The sum of the exterior angles of a polygon

The sum of the exterior angles of an n-sided polygon is 360°

For example, the sum of the interior angles of a polygon is equal to 3 times the sum of its exterior angles. How many polygons does it have?

think:

1. Each exterior angle of a polygon is equal to the interior angle adjacent to it. How many sides is this polygon?

2. Is there a polygon whose exterior angles are equal to 1/5 of the adjacent interior angles?

3. Is there a polygon whose interior angles are equal to 1/5 of the adjacent exterior angles?

4. If the number of sides of two polygons differs by 1, what are the similarities and differences in the sum of their interior angles and the sum of their exterior angles?

The sum of interior angles and the sum of exterior angles of polygons PPT, part 4 content: Discuss:

1. If the sides of a polygon are equal, must its interior angles be equal?

2. If the interior angles of a polygon are all equal, must its sides be equal?

Think about it:

Definition: A polygon with all equal interior angles and equal sides in a plane is called a regular polygon.

Features: Their sides ( )

Their angles ( )

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"Sum of Interior Angle and Sum of Exterior Angle of Polygon" PPT:

"The sum of the interior angles and the sum of the exterior angles of a polygon" PPT Part 1: Make a guess Xiao Ming has an idea: The 2008 Olympic Games will be held in Beijing. How meaningful it would be to design a polygonal flower bed whose interior angle sum is 2008! Can Xiao Ming’s idea be realized? ..

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Update Time: 2024-11-26

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