Math 1 March 16th

What you need today in class:

1. Pick up a calculator

2. Turn in Homework – page 13

WARM-UP: You DO NOT have to copy the problem, but do show your work!!

1. Calculate the sum of the interior angles of a 15-gon.2. Calculate the measure of one angle of a regular 18-gon.

Announcement for Freshman:

• You must pass your MATH class and your ENGLISH class to be promoted to 10th grade.

• So, if you fail MATH OR ENGLISH, you will stay in 9th grade next year.

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

interior angles is (n – 2)(180°)

Ex. 1 Use the regular pentagon to answer the questions.

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

B)Find the measure of ONE interior angle

540°

108°

Two more important terms

Exterior Angles

Interior Angles

In any convex polygon, the sum of the measures of the

exterior angles, one at each vertex, is 360°.

1

2

3

4

5

m m m m m 1 2 3 4 5 360

In any convex polygon, the sum of the measures of the

exterior angles, one at each vertex, is 360°.

1

3

2

m m m 1 2 3 360

If any convex polygon, the sum of the measures of the

exterior angles, one at each vertex, is 360°.

1

3

2

4

m m m m 1 2 3 4 360

Ex. 2 Find the measure of ONE exterior angle of a regular hexagon.

60°

sum of the exterior anglesnumber of sides

3606

Ex. 3 Find the measure of ONE exterior angle of a regular heptagon.

51.4°

sum of the exterior anglesnumber of sides

3607

Go to page 14 RegularPolygon

Interior AngleSum

Measure of ea. Interior

Exterior Angle Sum

Measure of ea. Exterior

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

Decagon

Dodecagon

N-gon

Assignment

• Page 18–Questions 1-12 and 15-18

Ex. 4 Each exterior angle of a polygon is 18. How many sides does it have?

n = 20

angleexterior sides ofnumber

anglesexterior theof sum

18360

n

Ex. 5 The sum of the measures of five interior angles of a hexagon is 535. What is the measure of the sixth angle?

185°

Ex. 6 The measure of the exterior angle of a quadrilateral are x, 3x, 5x, and 3x. Find the measure of each angle.

30°, 90°, 150°, and 90°

Ex. 7 If each interior angle of a regular polygon is 150, then how many sides does the polygon have?

n = 12