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3.4: The Polygon Angle-Sum Theorem

3.4: The Polygon Angle-Sum Theorem. Objective: To classify polygons, and to find the sums of interior and exterior angles of polygons. GOOD MORNING!!! It’s going to be a good day  . Polygon:. Closed plane figure At least 3 sides that are segments Sides intersect only at endpoints

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3.4: The Polygon Angle-Sum Theorem

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  1. 3.4: The Polygon Angle-Sum Theorem Objective: To classify polygons, and to find the sums of interior and exterior angles of polygons

  2. GOOD MORNING!!! It’s going to be a good day 

  3. Polygon: • Closed plane figure • At least 3 sides that are segments • Sides intersect only at endpoints • Adjacent sides are NOT collinear POLYGONS NOT POLYGONS

  4. TO NAME A POLYGON: • Start at any vertex • List vertices consecutively Name the polygon. Name the sides and angles. B A C E D

  5. Common Polygons:

  6. Convex vs. Concave CONVEX POLYGON • No diagonal with points outside polygon CONCAVE POLYGON • At least one diagonal outside polygon

  7. POLYGON-ANGLE-SUM THEOREM The sum of the measures of angles in an n-gon : (n-2)180 Example: Find the sum of the measures of a 15-gon.

  8. Finding missing angle measures • Figure out what the sum of the interior angles should be • Add up expressions and set them equal to the sum from part one. EXAMPLE: Find y: y° 120° 85° 53°

  9. Example: The sum of the measures of a given polygon is 720. How many sides are in the polygon? 2.Pentagon ABCDE has 5 congruent angles. Find the measure of each angle.

  10. Polygon-Exterior-Angle Sum Theorem The sum of the measures of exterior angles of a polygon is ALWAYS 360⁰. Example: What is the sum of exterior angles for a 500-gon?

  11. EQUILATERAL POLYGON:All sides EQUIANGULAR POLYGON:All angles REGULAR POLYGON: equilateral and equiangular ONE Interior Measure:ONE Exterior measure:

  12. Examples: The sum of the measures of angles of a polygon with n sides is 1980. Find n, the number of sides. 2. Find the measures of one interior angle and one exterior angle of a REGULAR hexagon. 3. The measure of an exterior angle of a regular polygon is 30⁰. What is the measure of an interior angle? How many sides are there?

  13. TYPE 2: Write and answer the following on a separate piece of paper. (2 points each question) • Find the sum of the interior and exterior angles of an octagon. • Find the measure of one interior angle and one exterior angle of a REGULAR 15-gon. • The sum of the interior angles of a polygon is 4680°. Find the number of sides.

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