Download Geometry Lesson 6.1.notebook

Geometry Lesson 6.1.notebook
February 12, 2015
BELL RINGER
Write an inequality for the range of values of x.
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Geometry Lesson 6.1.notebook
February 12, 2015
Angles of Polygons
A diagonal of a polygon is a segment that connects any two nonconsecutive vertices.
Remember that a triangle's angles add up to 180.
quadrilateral
4 sides­ 2 triangles
2 triangles­ so sum of all
interior angles of a quadrilateral is 2(180)=360
pentagon
5 sides­ 3 triangles
3 triangles­ so sum of all
interior angles of a pentagon is 3(180)=540
hexagon
6 sides­ 4 triangles
4 triangles­ so sum of all
interior angles of a hexagon is
4(180)=720
This leads us to a formula for finding the sum of the interior angles of an n­sided convex polygon is: 2
Geometry Lesson 6.1.notebook
February 12, 2015
a. Find the sum of the measures of the interior angles of a convex heptagon.
b. Find the measure of each interior angle of quadrilateral ABCD.
c. Find the sum of the measures of the interior angle of a convex octagon.
d. Find the measure of each interior angle of pentagon HJKLM.
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Geometry Lesson 6.1.notebook
February 12, 2015
e. Find the measure of each interior angle of a regular hexagon.
Finding the Number of Sides of a Regular Polygon Given the Measure of an Interior Angle
The measure of an interior angle of a regular polygon is 135. Find the number of sides of the polygon.
1. Using the same formula for the sum of the angles will allow us to do this. We will be solving for n.
The polygon has n sides, but each angle is 135 so the sum of the angles will be 135n.
f. The measure of an interior angle of a regular polygon is 144. Find the number of sides of the polygon.
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Geometry Lesson 6.1.notebook
February 12, 2015
Earlier we determined that the measures of the interior angle of a regular hexagon was 120. If that is true then what is the measure of each exterior angle of that same hexagon (angles 1 through 6)?
The sum of the exterior angles of any polygon, no matter what the size is always 360.
a.
b. Find the measure of each exterior angle of a regular dodecagon.
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Geometry Lesson 6.1.notebook
February 12, 2015
P. 394 12­37, 45, 46
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