1. Angle Properties in Polygons
Topic 3
Angle Properties in Polygons
Unit 2 Topic 3

2. Explore Complete the following chart. What do you notice? Polygon
Number of Sides
Diagram
Number of Triangles
Sum of Angle Measures
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon

3. Explore Polygon Number of Sides Diagram Number of Triangles
Sum of Angle Measures
Triangle 3 1
180⁰
Quadrilateral 4 2
360⁰
Pentagon 5
540⁰
Hexagon 6
720⁰
Heptagon 7
900⁰
Octagon 8
1080⁰
Can you come up with a way to calculate the sum of the angle measures based on the number of sides in the polygon?

4. Information You should notice that
The sum of the angle measures in the polygon is equal to 180⁰ X (number of sides – 2)

5. Example 1
Try this on your own first!!!!
Determining the sum of the measure of the interior angles.
Determine the sum of the measures of the interior angles of a
hexagon b) 15-sided polygon
(pentadecagon)

6. Example 1: Solution hexagon b) 15-sided polygon (pentadecagon)
A hexagon has 6 sides.
hexagon b) 15-sided polygon
(pentadecagon)

7. Example 2 Determine the measure of each interior angle of a regular:
Try this on your own first!!!!
Determining the measure of each interior angle
Determine the measure of each interior angle of a regular:
a) pentagon b) octagon

8. Example 2: Solution a) pentagon b) octagon 5 sides 8 sides
5 equal angles
8 equal angles

9. Try this on your own first!!!!
Example 3
Determining how many sides
Determine how many sides a polygon must have if its interior angles add up to:
a) 3060⁰ b) 1800 ⁰

10. Example 3: Solution
a) 3060⁰ b) 1800 ⁰

11. Example 4 Determine the value of x. Determine the value of each
Try this on your own first!!!!
Example 4
Determining the missing angles
Determine the value of x.
Determine the value of each
internal angle. A B C D 4x
3x + 20
2x + 40
x + 20

12. Example 4: Solution Determine the value of x.
Determine the value of each
internal angle. A B C D 4x
3x + 20
2x + 40
x + 20

13. Hint: Try drawing a picture.
Try this on your own first!!!!
Example 5
Floor tile designs
A floor tiler designs custom floors using tiles in the shape of regular polygons. Can the tiler use regular octagons and squares to tile a floor, if they have the same side length?
Hint: Try drawing a picture.

14. Example 5: Solution
Yes he can.
Etc, etc…

15. Example 6 Determine the values of a, b, c, and d.
Try this on your own first!!!!
Example 6
Determining missing angles
Determine the values of a, b, c, and d. a b c d

16. Example 6: Solution
1. We have a regular hexagon. The sum of all the interior angles is:
The value of each interior angle is: a b c d
120⁰
60⁰
3. All three angles in a triangle must add to 180⁰, so the third angle must be 60⁰.
60⁰
60⁰
120⁰
60⁰
2. We can find the blue angles by noting that they lie on a straight line with 120⁰, making them supplementary.
3. Using corresponding angles, angle d is 60⁰.

17. Need to Know:
The sum of the measures of the interiors angles of a polygon with n sides is determined using
To determine the measure of each interior angle in a regular polygon, divide the sum of the interior angles by the number of angles (same as the number of sides).
The sum of the measures of the interior angles of a polygon is 360.
You’re ready! Try the homework from this section.