Answer each question as indicated. What is the sum measures of the interior angles of a triangle? Answer: 180 

Answer each question as indicated. What is the measure of each angle of an equilateral triangle? Answer: 60 

Answer each question as indicated. What is the sum measures of the interior angles of a quadrilateral? Answer: 360 

 Determine the sum of the measures of the interior and exterior angles of the triangle.  Determine the sum of the measures of the interior and exterior angles of a quadrilateral.  Make generalizations on the sum of the measures of the interior and exterior angles of a polygon.

EXERCISES TELL WHETHER OR NOT EACH OF THE FOLLOWING IS A POLYGON.

Exercises TELL WHETHER A POLYGON IS CONVEX OR NOT.

POLYGONS and its parts Review

POLYGON PARTS

Side - one of the line segments that make up the polygon. Vertex - point where two sides meet. Two or more of these points are called vertices.

POLYGON PARTS Diagonal - a line connecting two vertices that isn't a side.

ANGLE SUM MEASURES

Angle Sum measure of the interior angles of a polygon PolygonNo. of sidesNo. of non- overlapping diagonals No. of Triangles formed Angle Sum measure triangle3011 x 180°or 180° Quadrilateral4122 x 180°or 360° Pentagon5233 x 180°or 540° N- gonnn-3n-2(n-2)180°

Examples:  1. What is the sum of the measures of the interior angles of a convex polygon with  a. 11 sides  b. 15 sides Solutions: a. S a = (n – 2) 180 ⁰ = (11 – 2) 180 ⁰ = 9(180 ⁰ ) = 1620 ⁰

Examples:  1. What is the sum of the measures of the interior angles of a convex polygon with  a. 11 sides  b. 15 sides Solutions: b. Sa = (n – 2) 180 ⁰ = (15 – 2) 180 ⁰ = 13(180 ⁰ ) = 2340 ⁰

Examples:  2. Find the sum of the measures of the interior angles of a convex heptagon. Solutions: b. Sa = (n – 2) 180 ⁰ = (7 – 2) 180 ⁰ = 5(180 ⁰ ) S = 900 ⁰

Examples:  3. How many sides does a convex polygon have if the sum of the measures of its interior angles is 1440 ⁰ ? Solutions: b. Sa = (n – 2) 180 ⁰ 1440 ⁰ = (n – 2) 180 ⁰ 1440 = 180 ⁰ n – 360 ⁰ n = n = 10 The polygon has 10 sides.

FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN ° S=(n-2) =180n = 180n 1620 = 180n n= 9

FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN ° n =(S  180) + 2 = (1260  180) + 2 = n= 9

QUIZ

A. FIND THE SUM OF THE MEASURES OF THE VERTEX ANGLES FOR EACH POLYGON gon gon gon

B. FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN ° °

Angle Sum Measures of the Exterior Angles of a Polygon LESSON 7

POLYGON PARTS Interior Angle - Angle formed by two adjacent sides inside the polygon. Exterior Angle - Angle formed by two adjacent sides outside the polygon.

Investigate   1,  2 and  3 are interior angles.   4,  5 and  6 are exterior angles   1 +  4 = 180°   2 +  5 = 180°   3 +  6 = 180°

 If m  1= 70, what is the measure  4?  m  4= 110  If m  2 = 80, what is the m  5?  m  5= 100  If m  3 = 30, what is the m  6?  m  6=

The sum of the exterior angles of an n-gon is 360°  m  4= 110  m  5= 100  m  6= 150  m  2 + m  4 + m  6=

160° 70° 120° 70° 60° 110° 20° 60° 110° 60° + 60 ° ° + 20 ° + 110° = 360°

Angle Sum measure of the exterior angles of a polygon PolygonNo. of sides Angle Sum measure (interior angles) Measure of EACH INTERIOR angle of a regular n-gon Angle Sum measure (exterior angles) Measure of EACH exterior angle of a regular n-gon triangle31 x 180°or 180° 180° 3 360° 3 Quadrilat eral 42 x 180°or 360° 360° 4 360° 4 Pentagon53 x 180°or 540° 540° 5 360° 5 N- gonn(n-2)180° n 360° n

Examples:  1. How many degrees are there in each of the exterior angle of a regular hexagon? Solution: E a = E a = = 60

FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE MEASURE OF THE EXTERIOR ANGL E IS GIVEN 1. 30° 2. 10°

QUIZQUIZ

FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN ° °

FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE MEASURE OF THE EXTERIOR ANGLE IS GIVEN 1. 24° 2. 45°