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3.3: Angles of Polygons

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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

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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.

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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.

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

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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.

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Practice Find the value of x.

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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.

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

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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 105 0 and (105+26)=13 1 0

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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.

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