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Published byGwenda Sanders Modified over 8 years ago
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G.10 The student will solve real-world problems involving angles of polygons
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POLYGON a closed figure that is the union of line segments in a plane. A polygon has three or more sides. A polygon has the same number of angles as sides. A regular polygon is a polygon that is both equilateral and equiangular.
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These figures are not polygonsThese figures are polygons POLYGONS
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CLASSIFICATIONS OF A POLYGON Convex: A polygon with no angles measuring more than 180 No line containing a side of the polygon contains a point in its interior Concave: A polygon that has at least one angle that measures more than 180 (a reflex angle) A polygon for which there is a line containing a side of the polygon and a point in the interior of the polygon. Has no indentations. Like a cave. Has indentations.
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TYPES OF REGULAR POLYGONS
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Interior Angle of a Polygon For example, ∆ ABC has interior angles: ABC, BAC, BCA The interior angles of a polygon are the angles inside the polygon, formed by two adjacent sides.
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SUM OF INTERIOR ANGLES OF A POLYGON =180(n -2) (n is the number of sides) Example 1: Find the number of degrees in the sum of the interior angles of an octagon. Example 2: How many sides does a polygon have if the sum of its interior angles is 720°?
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DETERMINING EACH INDIVIDUAL ANGLE IN A REGULAR POLYGON Let’s investigate using a regular pentagon: Since the pentagon is a regular pentagon, the measure of each interior angle will be the same
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(n is the number of sides) Example 3: Find the number of degrees in each interior angle of a regular dodecagon. Example 4: Each interior angle of a regular polygon measures 135°. How many sides does the polygon have ?
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Exterior Angle of a Polygon For example, ∆ ABC has exterior angle: ACD. It forms a linear pair with ACB. An exterior angle of a polygon is an angle that forms a linear pair with an interior angle. It is an angle outside the polygon formed by one side and one extended side of the polygon. A B C D Exterior Angle Interior Angles
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SUM EXTERIOR ANGLES OF ANY POLYGON = 360°
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