WARM UP: 0 You know the meaning of equilateral. What do you think an equiangular polygon is? 0

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