8.1 – Find Angle Measures in Polygons

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

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

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

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

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

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

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

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

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

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

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

2. Find x. 180(n – 2) 180(4 – 2) 180(2) 360° 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° 180(n – 2) = 2340 ? 180n – 360 = 2340 180n = 2700 2340° 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 180n – 360 = 6840 180n = 7200 n = 40

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

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

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

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

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

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

Sum of Angles Each angle Exterior 360° n 360°

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° n 360° 12 30° = = ?

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

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

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

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

HW Problem #24 180(n – 2) n 156 = 1 156n = 180n – 360 0 = 24n – 360 Section Page # Assignment Spiral 8.1 510-512 #3-11 odd, 12, 15, 16, 19, 24, 25, 29 1-5 #24 180(n – 2) n 156 = 1 156n = 180n – 360 0 = 24n – 360 360 = 24n 15 = n