Download presentation

1
Angles in Polygons

2
**Sums of Interior Angles**

Triangle Quadrilateral Pentagon = 2 triangles = 3 triangles Hexagon Octagon = 4 triangles Heptagon = 5 triangles = 6 triangles

3
Convex Polygon # of Sides # of Triangles Sum of Interior Angles Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon n-gon 3 1 180 4 2 360 5 3 540 6 4 720 7 5 900 8 6 1080 n n – 2 180•(n – 2)

4
**Find the measure of the missing angle in the figure below**

x = 360 100 135 70 x 305 + x = 360 x = 55 quadrilateral

5
**5(20) - 5 m1 = = 95 pentagon 1 2 3 110 (5x - 5) (4x + 15)**

Find m1. m1 = 5(20) - 5 = 95 5x x x = 540 17x + 200= 540 pentagon 17x = 340 x = 20

6
Interior Angles 1 2 3 4 5 6 Exterior Angles

7
**Sums of Exterior Angles**

1 2 3 4 5 6 180 180 180•3 = 540 180 Sum of Interior & Exterior Angles = 540 Sum of Interior Angles = 180 Sum of Exterior Angles = 540- 180= 360

8
**Sums of Exterior Angles**

180 180 180 180•4 = 720 180 Sum of Interior & Exterior Angles = 720 Sum of Interior Angles = 360 Sum of Exterior Angles = 720- 360= 360

9
**Sum of Exterior Angles 180•5 = 900 Sum of Interior & Exterior Angles =**

180 180 180 180 180 180•5 = 900 Sum of Interior & Exterior Angles = 900 Sum of Interior Angles = 540° Sum of Exterior Angles = 900- 540= 360

10
**Sum of Exterior Angles 180•6 = 1080**

180 180 180 180 180 180 180•6 = 1080 Sum of Interior & Exterior Angles = 1080 Sum of Interior Angles = 720° Sum of Exterior Angles = 1080- 720= 360

11
**Sums of Exterior Angles**

Polygon # of Sides Interior + Exterior Interior Angles Exterior Angles Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 540 180 360 720 360 360 900 540 360 1080 720 360 Sum of Exterior Angles is always 360!

12
**Angles of Regular Polygons**

Sum of the Interior Angles 180(n – 2) Sum of the Exterior Angles Always 360! 180(n – 2) Each Interior Angle n Each Exterior Angle 360 n

13
**What is the measure of each angle?**

Find the sum of the measures of the interior angles of a regular dodecagon. n = 12 180•(n – 2) = 180•(12 – 2) = 180•(10) all 12 angles = 1800 What is the measure of each angle? 1800 each angle = 150 12

14
**The sum of the interior angles of a convex polygon is 1440.**

How many sides does the polygon have? 180•(n – 2) = 1440 180n – 360 = 1440 180n = 1800 n = 10 10 sides

15
Exterior Angles What is the measure of each exterior angle of a regular hexagon? 6 sides 360 = 60 6

16
**The measure of each exterior angle of a regular polygon is 20**

The measure of each exterior angle of a regular polygon is 20. How many sides does it have? 360 = 18 20 The measure of each interior angle of a regular polygon is 120. How many sides does it have? = 60 360 = 6 60 exterior angle

17
**Find the sum of the interior angles of a**

100-gon! Find the sum of the exterior angles of a 100-gon. Find the measure of each interior angle of a Find the measure of each exterior angle of a

Similar presentations

Presentation is loading. Please wait....

OK

Concept: Angle Measures in Polygons

Concept: Angle Measures in Polygons

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google