1. 6-1: Angles of Polygons
yes no
Definition of a quadrilateral - a closed figure with four sides and four vertices.
Are these quadrilaterals? Yes or no?

2. Name a quadrilateral Name in order of the vertices. Quadrilateral HOPE
Quadrilateral OPEH
Quadrilateral PEHO
Quadrilateral EHOP
Quadrilateral HEPO
Quadrilateral POHE H O E P

3. BL and LU are consecutive sides Nonconsecutive- not next to
Consecutive- next to
BL and LU are consecutive sides
Nonconsecutive- not next to
BL and EU are nonconsecutive sides
Diagonals - segment whose endpoints are nonconsecutive vertices.
BU and EL are diagonals B L E U

4. Theorem 6.1: Interior Angle Sum
If a convex polygon has n sides and S is the sum of the measures of its interior angles, then S = 180(n - 2).
Convex Polygon
Number of Sides
Number of Triangles
Sum of Angle Measures
Triangle 3 1
1 x 180 = 180
Quadrilateral 4 2
2 x 180 = 360
Pentagon 5
3 x 180 = 540
Hexagon 6
4 x 180 = 720
Heptagon 7
5 x 180 = 900
Octagon 8
6 x 180 = 1080

5. Example
The measure of an interior angle of a regular polygon is Find the number of sides in the polygon.
S = 180 (n – 2)
S = 135n
135n = 180 (n – 2)
135n = 180n – 360
-45n = -360
n = -360/-45 = There are 8 sides

6. Example
Find the measure of M in quadrilateral KLMN if mK = 2x, mL = 2x, mM = 2x-20, and mN = 3x + 20.
2x + 2x + 2x x + 20 = 360
9x = 360
x = 40
Am I done?
No!!!
mM = 2x-20 = 2(40)-20 = = 60

7. Theorem 6.2: Exterior Angle Sum
If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360.
m1 + m2 + m3 + m4 + m5 = 360 1 5 4 3 2

8. Example
Find the measures of an exterior angle and an interior angle of a convex dodecagon.
Hint: Dodecagon has 12 sides.
Exterior Angle measure = 360/12 = 30
Interior Angle measure = (180*10)/12 = 150

9. Try these on Page 321 #1-6 540 3 4 mT = mV = 46; mU = mW = 134
60, 120
20, 160

10. Homework #37
P odd, 39-41