1. Finding the Measure of Angles in Polygons

2. In a regular polygon, all the angles and sides are the same size.
To find the measure of a single angle:
Divide the Sum by the Number of Sides.
For example:
In a regular pentagon, the sum of the interior angles is 540 and the number of sides is 5.

3. In your notebooks: Find the measure of a single angle in each regular polygon.
180
720
360
To find the measure of a single angle:
Divide the Sum of the Interior Angles by the Number of Sides/Angles.

4. To Find the Missing Angle, with an irregular polygon:
Step 1: Find the sum of the interior angles for the polygon (count number of sides, and use formula)
Step 2: Add up all the given angles.
Step 3: Set two sums equal to each other.
Step 4: Solve for x

5. To Find the Missing Angle:
Step 1: Find the sum of the interior angles for the polygon
(ignore given angles, count number of sides, and use formula)
180(n – 2) =
180(7 – 2) =
180(5) =
900° 2 1
135 x 3 90 7
100
145 4 95
170 6 5

6. To Find the Missing Angle:
Step 2: Add up all the given angles.
x =
735 + x
135 x 90
100
145 95
170

7. To Find the Missing Angle:
Step 3: Set two sums equal to each other.
Step 4: Solve for x
(you will need to subtract)
735 + x = 900
x = 165°
135 x 90
100
145 95
170

8. Practice with One Angle in Regular and Irregular Polygons
Each of you will be working on a mini-worksheet titled: “Find the Measure on One Angle in a Regular Polygon.”
Use the first part of the notes.
When you finish, there will be a worksheet up front called, “Angles and Polygons: C.”
This worksheet is practice for IRREGULAR polygons.
Use the second part of the notes.
BOTH are DUE in class.