then: you name and classified polygons now: 1.find and use the sum of the measures of the interior...
TRANSCRIPT
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: