WARM UP:
0You know the meaning of equilateral. What do you think an equiangular polygon is?
0
6.1 - The Polygon Angle-Sum TheoremsI can find the sum of the measures of the interior angles of a polygon. I can find the sum of the measures of the exterior angles of a polygon.
Theorem 6-1
0The sum of the interior angle measures of a polygon depends on the number of sides the polygon has.
Polygon Angle-Sum Theorem
The sum of the measures of the ______________of an n-gon is ______________________.
Problem: Finding a Polygon Angle Sum
0What is the sum of the interior angle measures of a heptagon?
Problem: Finding a Polygon Angle Sum
0What is the sum of the interior angle measures of a 17-gon?
0The sum of the interior angle measures of a polygon is 1980. How can you find the number of sides in the polygon?
Problem: Finding a Polygon Angle Sum
0What is the sum of the angle measures of a 10-gon?
Corollary to the Polygon Angle-Sum Theorem
The measure of _____________________________________n-gon is _________________.
Problem: Using the Polygon Angle-Sum
Theorem0The common housefly, Musca domestica, has eyes that
consist of approximately 4000 facets. Each facet is a regular hexagon. What is the measure of each interior angle in one hexagonal facet?
Problem: Using the Polygon Angle-Sum
Theorem0What is the measure of each interior angle in a regular
nonagon?
Problem: Using the Polygon Angle-Sum
Theorem0Marcy creates a floor tile pattern using squares,
regular hexagons, and regular dodecagons. What is the measure of each angle in one regular dodecagon?
Problem: Using the Polygon Angle-Sum
Theorem0What is m<Y in pentagon TODAY?
Problem: Using the Polygon Angle-
Sum Theorem0What is m<G in quadrilateral EFGH?
Problem: Using the Polygon Angle-Sum
Theorem0What is m<D in quadrilateral ABCD?
Theorem 6 – 2 Polygon Exterior Angle-Sum Theorem
The sum of the measures of the __________________________of a polygon, one at each vertex, is ________.
Problem: Finding an Exterior Angle Measure
0What is m<1 in the regular octagon?
Problem: Finding an Exterior Angle Measure
0What is the measure of an exterior angle of a regular nonagon?
Problem: Finding an Exterior Angle Measure
0What is the measure of an exterior angle of a regular hexagon?
After: Lesson Check
1. What is the sum of the interior angle measures of an 11-gon?
2. What is the sum of the measures of the exterior angles of a 15-gon?
3. Find the measures of an interior angle and an exterior angle of a regular decagon?
Homework:Page 356, #7 – 23 all, 29, 33, 35