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3.3: Angles of Polygons

3.3: Angles of Polygons. What is a Polygon?. A polygon is a closed plane figure made up of three or more line segments that intersect only at their endpoints. In a regular polygon all the sides are congruent, and all of the interior angles are congruent.

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3.3: Angles of Polygons

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  1. 3.3: Angles of Polygons

  2. What is a Polygon? • A polygon is a closed plane figure made up of three or more line segments that intersect only at their endpoints. • In a regular polygon all the sides are congruent, and all of the interior angles are congruent. • Interior angle measures of a polygon: • The sum S of the interior angle measures of a polygon with n sides is

  3. Concave and Convex Polygons • A polygon is convex when every line segment connecting any two vertices lies entirely inside the polygon. • A polygon is concave when at least one line segment connecting any two vertices lies outside the polygon.

  4. Finding the Sum of Interior Angle Measures • Find the sum of the interior angle measures of the school crossing sign. • The sign is in the shape of a pentagon. It has 5 sides.

  5. Practice Find the sum of the interior angle measures of the green polygon. • The honey comb has 6 sides • The web has 7 sides

  6. Finding an Interior Angle Measure of a Polygon Find the value of x. • Step 1: The polygon has 7 sides. Find the sum of the interior angle measures. • Step 2: Write and solve an equation to find x.

  7. Practice Find the value of x.

  8. Real Life Application • Step 1: A hexagon has 6 sides. Find the sum of the interior angle measures. • Step 2: Divide the sum by the number of interior angles, 6. • A cloud system discovered on Saturn is in the approximate shape of a regular hexagon. Find the measure of each interior angle of the hexagon.

  9. Exterior Angle Measures of a Polygon • The sum of the measures of the exterior angles of a convex polygon is 3600. • Algebra • w+x+y+z=3600

  10. Finding Exterior Angle Measures Find the measures of the exterior angles of each polygon. • Write and solve an equation for z • Write and solve an equation for x The exterior angles measures are 1050 and (105+26)=1310

  11. Practice • Find the measures of the interior angles of the polygon. • Write and solve an equation to find x. The exterior angle measures are 900, 450, 900, 900, and 450.

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