Recommended textbook solutionsCalculus7th EditionBruce H. Edwards, Larson, Robert P. Hostetler 10,461 solutions Algebra and Trigonometry5th EditionRobert F. Blitzer 10,851 solutions Algebra and Trigonometry1st EditionJay Abramson 6,339 solutions Algebra and Trigonometry9th EditionMichael Sullivan 10,535 solutions Presentation on theme: "Lesson 8-1 Angles of Polygons."— Presentation transcript: 1 Lesson 8-1 Angles of Polygons 2
5-Minute Check on Lesson 7-4
3 5-Minute Check on Lesson 7-4 4 Objectives Find the sum of the measures of the interior angles of a polygon Sum of Interior angles = (n-2) • 180 One Interior angle = (n-2) • 180 / n Find the sum of the measures of the exterior angles of a polygon Sum of Exterior angles = 360 One Exterior angle = 360/n Exterior
angle + Interior angle = 180 5 Vocabulary Diagonal – a segment that connects any two nonconsecutive vertices in a polygon.
6 Angles in a Polygon 1 2 3 4 5 6 7 8 Octagon n = 8
7 Sum of Interior Angles: so each interior angle is (n – 2) * 180
8 Polygons Sides Name Sum of Interior Angles One Interior Angle 9 Interior Angle Sum Theorem
10 Interior Angle Sum Theorem
11 SHORT CUT!! The measure of an interior angle of a regular polygon is 135. Find the number of sides in the polygon. Exterior angle
= 180 – Interior angle = 45 n = = = 8 Ext 12 Answer: The polygon has 10 sides. 13 Find the measure of each interior angle. 14 Subtract 8 from each side. 15 Find the measure of each interior angle.
16 At each vertex, extend a side to form one exterior angle.
17 Find the measures of an exterior angle and an interior angle of convex regular hexagon ABCDEF.
18 Polygon Hierarchy Polygons Quadrilaterals Parallelograms Kites
19 Quadrilaterals Venn Diagram
20 Quadrilateral Characteristics Summary 21 Summary & Homework Summary:
Homework: |