Find the measures of the three angles.

In ABC, m A = x°, m B = 3x°, and

m C = (4x – 12) ° .

ANSWER 24°, 72°, 84°

Do Now

If all the If all the s in a s in a ΔΔ add up to 180 add up to 180oo. Then . Then what about the what about the s in a quadrilateral s in a quadrilateral

and pentagon?and pentagon?

3 * 180 = 5403 * 180 = 540oo

How about a hexagon?How about a hexagon?

4 * 180 = 7204 * 180 = 720oo

2 * 180 = 3602 * 180 = 36000

# of sides

# of triangles

Sum of measures of

interior angles

3 1 1(180)=180

4 2 2(180)=360

5 3 3(180)=540

6 4 4(180)=720

n n-2 (n-2) • 180

If a convex polygon has n sides, then the sum of the measure of

the interior angles is

(n – 2)(180°)

If a regular convex polygon has n sides, then the measure of one of the interior angles is

n

n 180)2(

Ex. 1 Use a regular 15-gon to answer the questions.

A)Find the sum of the measures of the interior angles.

B) Find the measure of ONE interior angle

2340°

156°

Ex: 2 Find the value of x in the polygon

130

126

143

100

117

x

126 + 130 + 117 + 143 + 100 + x = 720

616 + x = 720

x = 104

Ex: 3 The measure of each interior angle is 150°, how many sides does the regular polygon have?

n

n 180)2(One interior angle

150180)2(

n

n

nn 150180)2(

nn 150360180 36030 n

12nA regular dodecagon

Two more important terms

Exterior Angles

Interior Angles

The sum of the measures of the

exterior angles of a convex polygon, one

at each vertex, is 360°.

1

2

3

4

5

m m m m m 1 2 3 4 5 360

1

3

2

m m m 1 2 3 360

The sum of the measures of the

exterior angles of a convex polygon, one

at each vertex, is 360°.

1

3

2

4

m m m m 1 2 3 4 360

The sum of the measures of the

exterior angles of a convex polygon, one

at each vertex, is 360°.

The measure of each exterior angle of a regular polygon is

n

360

Ex. 4 Find the measure of ONE exterior angle of a regular 20-gon.

18°

sum of the exterior anglesnumber of sides

360

20

Ex. 5 Find the measure of ONE exterior angle of a regular heptagon.

51.4°

sum of the exterior anglesnumber of sides

3607

Ex. 6 The sum of the measures of five interior angles of a hexagon is 625. What is the measure of the sixth angle?

95°

Let’s practice!

8.1 Worksheet

Look on the bottom of the

Worksheet