Lesson 8-1 Angles of Polygons Lesson 3-4: Polygons.

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Presentation transcript:

Lesson 8-1 Angles of Polygons Lesson 3-4: Polygons

Convex Polygon Diagonals Diagonals of a Polygon: A segment connecting nonconsecutive vertices of a polygon Determine the least number of triangles that can be formed from each polygon by drawing diagonals. What correlation can be made between the number of triangles and the number of sides of the polygon? Lesson 3-4: Polygons

3 sides 4 sides 5 sides 6 sides 8 sides Determine the least number of triangles that can be formed from each polygon by drawing diagonals. What correlation can be made between the number of triangles and the number of sides of the polygon? 3 sides 4 sides 5 sides 6 sides 8 sides __triangle __ triangles __ triangles __ triangles __triangles ____° ____° ____° ____ ° ____ ° The number of triangles is: If the sum of the interior angles of a triangle is 180°, what can we assume to be the sum of the interior angles of the polygons shown? What is the formula to find the sum of the interior angles of a convex polygon? Lesson 3-4: Polygons

Find the sum of the interior angles of each convex polygon. S = n = # of sides A) Quadrilateral B) 11-gon Lesson 3-4: Polygons

Find the measure of each interior angle using the given information. (6x – 4)° (2x + 8)° (2x + 8)° (6x – 4)° Lesson 3-4: Polygons

Find the measure of each interior angle using the given information. B A (2x + 15)° (3x - 20)° x° (x + 15)° C D Lesson 3-4: Polygons

Sum of the Exterior Angles = 60° 90° 90° 60° 60° 90° 90° 100° 100° 108° 108° 108° 80° 80° 108° 108° Lesson 3-4: Polygons

Convex Polygon Formulas….. For a convex polygon with n sides: The sum of the interior angles is The sum of the exterior angles is The measure of one exterior angle is The measure of exterior angle + interior angle is Lesson 3-4: Polygons

Find the measure of the interior and exterior angle of each regular polygon. A) 30-gon Exterior Angle = Interior Angle = B) Pentagon C) 14-gon Lesson 3-4: Polygons

The measure of an interior angle of a regular polygon is given The measure of an interior angle of a regular polygon is given. Find the number of sides in each polygon. A) 144 B) 156 Lesson 3-4: Polygons