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3.4 Polygon Angle Sum Theorems

10/28 with practice on 10/29

I can name and classify a polygon given the number of sides and vertices.

I can find the interior angles of a polygon using the Polygon Angle Sum Theorem

I can find the exterior angle of a polygon using the Polygon Exterior Angle Sum Theorem

Learning Targets

Polygon : a polygon is a closed plane figure with at least three sides that are segments. The sides intersect only at their endpoints.

To name a polygon, you must name the vertices consecutively

EX:

Convex polygon: Has no diagonals with points outside the polygon.

Concave polygon: Has at least one diagonal with points outside the polygon.

EX

Part a is Convex part b is Concave

Polygon Classification3 sides-4 sides-5 sides-6 sides-

Polygon Classification(cont’d)7 sides -8 sides - 9 sides - 10 sides - 12 sides - N sides -

Polygon Angle Sum Theorem: The sum of the measures of the interior angles of any polygon is (n – 2)180, where n is the number of sides.

Ex. What is the sum of the measures of angles of a Decagon?Pentagon?

Find the sum of the measures of angles of an octagon

In your groups

Find x

The sum of the measures of the interior angles is 720. How many sides does it have?

Hint: Work backwards

In your groups

Polygon Exterior Angle Sum Theorem: The sum of the exterior angles of a polygon is 360 degrees. ALWAYS!

An Equilateral polygon has all sides congruent.

An Equiangular polygon has all angles congruent.

The following is SUPER IMPORTANT!!!A regular polygon has all equal angles and equal sides.

What is the measure of an exterior angle of a regular hexagon?

What is the measure of an interior angle of a regular dodecagon?

In your groups

The following is a regular polygon, find the missing measures

In your groups

In a regular polygon, the sum of an interior angle and exterior angle is 180

Homework In packet 3-4

Warmup – Grab your bookFor a regular nonagon

◦What is the measure of an interior angle?

◦What is the measure on an exterior angle?

Day 2 for 3.4

Go over 3-4 Packet.

P.147 #16-21

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