Triangle Sum Theorem

By: Jeffrey McAven

Triangle

•What is the measure of the interior angles of a Triangle?

180°

Rectangle

•What is the measure of the interior angles of a Rectangle?

Hint: How many triangles are there in a rectangle?

360° (180 for each triangle)

180°

180°

Does this work for ANY shape

•Any ideas how I might find the measure of the Interior angles for a random figure?

3 triangles

540° 4 Triangles720°

What is the Formula?

•After talking about the previous slides can you think of a possible formula?

(n-2)180 = the sum of the interior angles

n is the number of sides on any figure

Regular polygon: all sides and angle measurements are equal.

Lets Practice shall we.....

Tell me how many triangles and what the sum on the interior angles would be.

4 Sides

(4-2)180 = 360

Now what if I just tell you the amount of side??

Decagon (10 sides)

Nonagon (9 sides)

Dodecagon (12 Sides)

18-gon

(10-2)180 = 1,440

(9-2)180 = 1,260

(12-2)180 = 1,800

(18-2)180 = 2,880