1 / 16

2.6

2.6. What is Its Measure? Pg. 22 Interior Angles of a Polygon. 2.6 – What is Its Measure?_____________ Interior Angles of a Polygon

louis
Download Presentation

2.6

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 2.6 What is Its Measure? Pg. 22 Interior Angles of a Polygon

  2. 2.6 – What is Its Measure?_____________ Interior Angles of a Polygon In an earlier chapter, you discovered that the sum of the interior angles of a triangle is always 180°. But what about the sum of the interior angles of other polygons, such as hexagons or decagons? Consider these questions today as you investigate the angles of all polygons.

  3. Angle inside a shape Angle outside a shape 1 2

  4. 1 180° 2 360° 3 540° 4 720° 5 900°

  5. 6 1080° 7 1260° 8 1440° n – 2 180(n – 2) n-gon

  6. 180(n – 2) n 180(n – 2)

  7. 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 __________________ Polygon Sum = __________ 900°

  8. 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 __________________ Polygon Sum = __________ 5040°

  9. 2. Find the indicated variable. 180(n – 2) 1 180(5 – 2) 5 180(3) 540° 2 540° 4 x + 90 +143 + 77 + 103 = 540 3 x + 413 = 540 x = 127°

  10. 1 180(n – 2) 7 2 180(7 – 2) 6 900° 3 5 4 3m + 501 = 900 3m = 399 m = 133°

  11. 3. Given the sum of the measures of the interior angles of a polygon, find the number of sides. 2340° 180(n – 2) = 2340 180 180 ? n – 2 = 13 2340° n = 15

  12. 3. Given the sum of the measures of the interior angles of a polygon, find the number of sides. 6840° 180(n – 2) = 6840 180 180 ? n – 2 = 38 6840° n = 40

  13. 4. Given the number of sides of a regular polygon, find the measure of each interior angle. 180(n – 2) 180(5 – 2) = = n 5 540 180(3) = = 108° 5 5

  14. 18 sides 180(n – 2) 180(18 – 2) 180(16) = = = n 18 18 2880 = 160° 18

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

  16. 108° 180(n – 2) 108 = n 1 180(n – 2) = 108n 180n – 360 = 108n 72n – 360 = 0 72n = 360 n = 5

More Related