 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.

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Presentation transcript:

 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.  Interior angle measures of a polygon:  The sum S of the interior angle measures of a polygon with n sides is

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.

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.

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

Finding an Interior Angle Measure of a Polygon  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. Find the value of x.

Practice Find the value of x.

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.

Exterior Angle Measures of a Polygon  The sum of the measures of the exterior angles of a convex polygon is  Algebra  w+x+y+z=360 0

Finding Exterior Angle Measures  Write and solve an equation for z  Write and solve an equation for x Find the measures of the exterior angles of each polygon. The exterior angles measures are and (105+26)=13 1 0

Practice  Find the measures of the interior angles of the polygon.  Write and solve an equation to find x. The exterior angle measures are 90 0, 45 0, 90 0, 90 0, and 45 0.