Unit 6 Lesson 1 Find Angle Measures in

Unit 6 Lesson 1 – Find Angle Measures in Polygons

Interior Angle: Angle inside a shape 2 1 2 Exterior Angle: Angle outside a shape 1 Line connecting two Diagonal: nonconsecutive vertices

# of sides Name of Polygon 3 triangle # of triangles formed from 1 vertex 1 Sum of the measures of interior angles 180°

# of sides Name of Polygon # of triangles formed from 1 vertex Sum of the measures of interior angles 4 quadrilateral 2 360°

# of sides 5 Name of Polygon pentagon # of triangles formed from 1 vertex 3 Sum of the measures of interior angles 540°

# of sides Name of Polygon 6 hexagon # of triangles formed from 1 vertex 4 Sum of the measures of interior angles 720°

# of sides Name of Polygon # of triangles formed from 1 vertex Sum of the measures of interior angles 7 heptagon 5 900° 8 octagon 6 1080° 9 nonagon 7 1260° 10 decagon 8 1440° n n-gon n– 2 180(n – 2)

The sum of the measures of the interior angles 180(n – 2) of a polygon are: ____________ The measure of each interior angle of a regular n-gon is: 180(n – 2) n

Interior Sum of Angles Each angle 180(n – 2) n

1. Find the sum of the measures of the interior angles of the indicated polygon. 180(n – 2) 180(7 – 2) 180(5) 900° heptagon Name _________ 900° Polygon Sum = _____

1. Find the sum of the measures of the interior angles of the indicated polygon. 30 -gon 180(n – 2) 180(30 – 2) 180(28) 5040° 30 -gon Name _________ 5040° Polygon Sum = _____

2. Find x. 540° 180(n – 2) 180(5 – 2) 180(3) 540° x + 90 +143 + 77 + 103 = 540 x + 413 = 540 x = 127°

2. Find x. 360° 180(n – 2) 180(4 – 2) 180(2) 360° x + 87 + 108 + 72 = 360 x + 267 = 360 x = 93°

3. Given the sum of the measures of the interior angles of a polygon, find the number of sides. 2340° ? 2340° 180(n – 2) = 2340 180 n – 360 = 2340 180 n = 2700 n = 15

3. Given the sum of the measures of the interior angles of a polygon, find the number of sides. 6840° 180(n – 2) = 6840 180 n – 360 = 6840 180 n = 7200 n = 40

4. Given the number of sides of a regular polygon, find the measure of each interior angle. 8 sides 180(n – 2) = 180(8 – 2) = 180(6) = 1080 = 135° n 8 8 8 135° ?

4. Given the number of sides of a regular polygon, find the measure of each interior angle. 18 sides 180(n – 2) 180(18 – 2) 180(16) 2880 = 160° = = = n 18 18 18

5. Given the measure of an interior angle of a regular polygon, find the number of sides. 144° 180(n – 2) 144 = 1 n 144 n = 180 n – 360 0 = 36 n – 360 = 36 n 144° 10 = n

5. Given the measure of an interior angle of a regular polygon, find the number of sides. 108° 180(n – 2) 108 = 1 n 108 n = 180 n – 360 0 = 72 n – 360 = 72 n 5=n

Use the following picture to find the sum of the measures of the exterior angles. c d 120° e 110° a 70° 130°b m a = 70° m b = 50° m c = 110° m d = 60° m e = 70° Sum of the exterior angles = 360°

The sum of the exterior angles, one from each 360° vertex, of a polygon is: __________ The measure of each exterior angle of a 360° n regular n-gon is: _____________

Exterior Sum of Angles Each angle 360° n

6. Find x. x + 137 + 152 = 360 x + 289 = 360 x = 71°

6. Find x. x + 86 + 59 + 96 + 67 = 360 x + 308 = 360 x = 52°

7. Find the measure of each exterior angle of the regular polygon. 12 sides 360° = 30° n 12 ?

7. Find the measure of each exterior angle of the regular polygon. 5 sides 360° = 72° n 5

8. Find the number of sides of the regular polygon given the measure of each exterior angle. 60° 360° = 60° 1 n 60 n = 360 n=6 60°

8. Find the number of sides of the regular polygon given the measure of each exterior angle. 24° 360° = 24° 1 n 24 n = 360 n = 15

KNOW THESE!! Interior Exterior Sum of Angles Each angle 180(n – 2) n 360° n

HW Problem LT 6. 1 Page # Assignment 510 -512 #3 -11 odd, 12, 15, 16, 19, 24, 25, 29 #24 180(n – 2) 156 = 1 n 156 n = 180 n – 360 0 = 24 n – 360 = 24 n 15 = n Due