Geo 6.1 Angles of Polygons
Name __________________________
Learning Objective: After this lesson, you should be able to successfully recognize and apply angle
relationships in polygons.
Standard: G.MG.1 Use geometric shapes, their measures, and their properties to describe objects.
Find the SUM of the measures of the interior angles of each convex polygon.
1. nonagon
2. heptagon
3. decagon
4. 11-gon
5. 14-gon
6. 17-gon
The measure of an interior angle of a regular polygon is given. Find the number of sides in the polygon.
7. 108
8. 156
9. 120
10. 144
11. 160
12. 150
Find the value of x and the measure of each interior angle.
13.
14.
16.
15.
17.
Find the measures of EACH INterior angle of each regular polygon.
18. quadrilateral
19. pentagon
20. dodecagon
Find the measure of EACH EXterior angle for each regular polygon.
21. octagon
22. nonagon
23. 12-gon
Find the measures of an exterior angle AND an interior angle given the number of sides of each regular
polygon. Round to the nearest tenth, if necessary.
24. 16
25. 30
26. 22
27. 24
28. 14
29. 40
Find the measure of angle 1 in each diagram.
30.
31.
32. ARCHITECTURE In the Uffizi gallery in Florence, Italy, there is a room built by Buontalenti called the Tribune
(La Tribuna in Italian). This room is shaped like a regular octagon.
What angle do consecutive walls of the Tribune make with each other?
33. ARCHEOLOGY Archeologists unearthed parts of two adjacent walls of an ancient castle.
Before it was unearthed, they knew from ancient texts that the castle was shaped like a regular polygon, but
nobody knew how many sides it had. Some said 6, others 8, and some even said 100. From the information
in the figure, how many sides did the castle really have?
Answers: 1. 1260 3. 1440 5. 2160 7. 5 9. 6 11. 18
13. 6x – 30 = 360, x = 65, mA = 115, mC = 115, mB = 65, mD = 65
15. 36x = 720, x = 20, mD = 140, mE = 140, mH = 140, mG = 140, mF = 80, mI= 80
17. 16x + 8 = 360, x = 22, mR = 128, mS = 52, mT = 128, mU = 52 19. 108 21. 45
27. 165, 15 29. 171, 9 31. 55 33. 15 sides
In the book, do pages 394 – 397, problems: 8, 9, 30, 32
23. 30
25. 168, 12