Bellwork If the measures of two angles of a triangle are 19 and 80, find

the measure of the third angle Solve (x-2)180=1980 Find the value of x

x+358

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FIND ANGLE MEASURES IN

POLYGONS

Section 8.1

The Concept By this point we’ve already discussed the special properties of

triangles Now we’re going to discuss some special properties of

polygons and then further these with special properties of polygons

DefinitionSince we are discussing polygons that have more than three sides,

we can now introduce the term… Diagonal

Segment that joins two nonconsecutive vertices

Geogebra

Interior & Exterior Angles of polygons

TheoremsTheorem 8.1: Polygon Interior Angles Theorem

The sum of the measures of the interior angles of a convex n-gon is (n-2)•180

Corollary to Theorem 8.1: Interior Angles of a Quadrilateral

The sum of the measures of the interior angles of a quadrilateral is 360o.

ExampleWhat is the sum of the interior angles of a decagon?

( 2) 180n T

ExampleFind the measure of the missing angle?

115

65

155130

95

x

TheoremsTheorem 8.2: Exterior Angles Theorem

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

ExampleFind the measure of the missing angle?

65

115

25

5085

x

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Practical ExampleThe base of a jewelry box is shaped like a regular hexagon.

What is the measure of each interior and exterior angle of the hexagon?

Homework

8.11, 2, 3-36 mult. 3

ExampleSolve for x?

101

95

3x+21

2x

161

177163

Most Important Points Definition of diagonal Interior angles of a Polygon Theorem Exterior angles of a Polygon Theorem