1. Lesson 12.3 Angles and Polygons
Essential Question: How do you find interior and exterior angle measures of polygons?

2. Before we start…

3. What is a polygon?
A closed figure whose line sides are line segments that intersect only at their endpoints.

4. What is a regular polygon?
A polygon whose sides are all the same length and whose angles are all the same measure

5. How are polygons identified?
Polygons are identified by their number of sides.
Number of Sides
Name 3
Triangle 4
Quadrilateral 5
Pentagon 6
Hexagon 7
Heptagon 8
Octagon 9
Nonagon 10
Decagon 12
Dodecagon

6. What is an interior angle?
An angle inside the polygon

7. How do you find interior angle measures in a polygon?
Use the formula: Sum of angle measures in an n-gon: 𝑛−2 ∙180° Measure of one angle in a regular n-gon: 𝑛−2 ∙180° 𝑛

8. Find the sum of the angle measures in a 9-gon.

9. Find the sum of the angle measures in a octagon.

10. Find the sum of the angle measures in a 15-gon.

11. Find the sum of the angle measures in a pentagon.

12. Find the sum of the angle measures in a hexagon.

13. Find the measure of one angle in a regular heptagon
Find the measure of one angle in a regular heptagon. Round to the nearest tenth of a degree.

14. Find the measure of one angle in a regular 15-gon
Find the measure of one angle in a regular 15-gon. Round to the nearest tenth of a degree.

15. Find the measure of one angle in a regular octagon
Find the measure of one angle in a regular octagon. Round to the nearest tenth of a degree.

16. Find the measure of one angle in a regular decagon
Find the measure of one angle in a regular decagon. Round to the nearest tenth of a degree.

17. Find the measure of one angle in a regular 20-gon
Find the measure of one angle in a regular 20-gon. Round to the nearest tenth of a degree.

18. What is an exterior angle?
When you extend a side of a polygon, the angle that is adjacent to the interior angle

19. How do you find the measure of an exterior angle?
The exterior angle and its adjacent interior angle form a straight angle. These two angles will add up to 180°

20. Find 𝑚∠1 in the diagram.

21. Find 𝑚∠1 in the diagram.

22. Find 𝑚∠3 in the diagram.

23. Find 𝑚∠5 in the diagram.

24. Sum of Exterior Angles
The sum of the measures of the exterior angles at the vertex of a convex polygon is 360°.

25. Find the unknown angle measure in the diagram.

26. Find the unknown angle measure in the diagram.

27. How do you find angle measures in polygons?

28. Ticket Out the Door
Find the missing angles.