G.10 The student will solve real-world problems involving angles of polygons.

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Presentation transcript:

G.10 The student will solve real-world problems involving angles of polygons

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.

These figures are not polygonsThese figures are polygons POLYGONS

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.

TYPES OF REGULAR POLYGONS

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.

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°?

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

(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 ?

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

SUM EXTERIOR ANGLES OF ANY POLYGON = 360°