Then: You name and classified polygons

Now: 1. Find and use the sum

of the measures of the interior angles of a polygon.

2. Find and use the sum of the measures of the exterior angles of a polygon.

One-Patch Quilt

6.1 ANGLES OF POLYGONS

http://0.tqn.com/d/quilting/1/0/f/d/-/-/gpa-veg-patch.jpg

PolygonNumber of Sides

Number of triangles

Sum of measures of interior angles

Triangle 3 1 1 x 180 = 180

Quadrilater

al

     

Pentagon      

Hexagon      

INVESTIGATE ANGLE SUMS IN POLYGONS

Conclusions1. Pattern:

2. Expression:

3. Side lengths affect the sum?

INVESTIGATE ANGLE SUMS IN POLYGONS

The sum of the interior angles of an n-sided convex polygon is (n-2) x 180.

Example: mA + mB + mC + mD + mE + mF =(6-2)(180) = 720

THEOREM 6.1: POLYGON ANGLES SUM

http://image.tutorvista.com/calc_images/image/math/polygon.jpeg

a. Find the sum of the measures of the interior angles of a convex heptagon.

b. Find the sum of the measures of the interior angles of a convex 15-gon.

EXAMPLE 1 A: FIND THE INTERIOR ANGLES SUM

a. Find the sum of the interior angles.

b. Solve for x.

c. Find the measure of each angle .

EXAMPLE 1 B: FIND THE MEASURE OF EACH INTERIOR ANGLE

http://moodle.tbaisd.org/pluginfile.php/68876/mod_book/chapter/50999/angle%20sum%20ex.jpg

a. Find the sum of the interior angles.

b. Solve for x.

c. Find the measure of each angle.

EXAMPLE 1 C: FIND THE MEASURE OF EACH INTERIOR ANGLE

ARCHITECTURE A mall is designed so that fi ve walkways meet at a food court that is in the shape of a regular pentagon. Find the measure of one of the interior angles of the pentagon.

EXAMPLE 2 A: INTERIOR ANGLES MEASURE OF REGULAR POLYGONS

for a regular dodecagon

EXAMPLE 2 B: FIND THE MEASURE OF EACH INTERIOR ANGLE

http://www.gazebocreations.com/images/ProductPropertySet/225x177/Gazebos-dodecagon-red-cedar-single-roof.jpg

Sum of interior angles = (n – 2) x 180Regular polygon:

Each angle of regular polygon x n = (n – 2) x 180

The measure of an interior angle of a regular polygon is 150. Find the number of sides.

EXAMPLE 3: FIND THE NUMBER OF SIDES OF A REGULAR POLYGON

The sum of the exterior angle measures of a convex polygon, one at each vertex, is 360.

Example: m1 + m2 + m3 +m4 + m5 = 360

THEOREM 6.2 POLYGON EXTERIOR ANGLES SUM

a. Find the value of x.

EXAMPLE 4: FIND THE EXTERIOR ANGLE MEASURES OF A POLYGON

b. Find the measure of each exterior angle of a regular dodecagon.

EXAMPLE 4:

p. 398-401 #12-24 evens, 25, 26-34 evens,

38, 40, 44, 46, 47, 54

6.1 ASSIGNMENT: