Bellwork Bellwork (on ½ sheet—turn in)(on ½ sheet—turn in)

• An angle of a triangle is 50. Find the measure of the angle formed by the angle bisectors of the other two angles.

• If the measure of each interior angle of a regular polygon is find the number of sides of a polygon.

172

7.4 Sum of the 7.4 Sum of the Exterior AnglesExterior Angles

Students will be able to find the Students will be able to find the sum of the exterior angles of a sum of the exterior angles of a polygon and one exterior angle polygon and one exterior angle

of a regular polygon.of a regular polygon.

Exterior Angles (defn)Exterior Angles (defn)• Name the exterior angle of this

triangle?

• What is true about the sum of an interior and exterior angle?

• How many exterior angles are in a heptagon?

DiscoverTogether we will discover the formula

for the sum of the exterior angles of a polygon.

Exterior Angle Summary Exterior Angle Summary (Toolbox!)(Toolbox!)

Se=360 E = 360

n

# of Diagonals Formula # of Diagonals Formula (Toolbox!)(Toolbox!)

• d =( 3)

2

n n

Example 1 Example 1 • Find the sum of the exterior angles of

a convex heptagon.

• What is the measure of an exterior angle of an equiangular heptagon?

Example 2Example 2• If the measure of an exterior angle

of a regular polygon is 15, how many sides does the polygon have?

Example 3Example 3• Find the measure of each interior

and exterior angle of a dodecagon.

Example 4Example 4• What is the name of an equiangular

polygon if the ratio of the measure of an interior angle to the measure of an exterior angle is 3:1?

Ticket to LeaveTicket to Leave• What is the measure of each interior

and exterior angle of a regular 18-gon?

HomeworkHomework• Pg. 309 # 3, 6, 8, 11b, 13, 14• Pg. 316 # 1, 3, 11-13• Quiz TOMORROW—Study All 5 Formulas!

Example 5Example 5A polygon has 54 diagonals, how many

sides does it have?

Extra CreditExtra Credit• In what polygon is the sum of the

measures of the exterior angles, one per vertex, equal to the sum of the measures of the angles of the polygon?

• Due Friday. Show all work for a full solution.

Extra CreditExtra Credit• In what polygon is the sum of the

measures of the exterior angles, one per vertex, equal to the sum of the measures of the angles of the polygon?

• Due Friday. Show all work for a full solution.

Extra CreditExtra Credit• In what polygon is the sum of the

measures of the exterior angles, one per vertex, equal to the sum of the measures of the angles of the polygon?

• Due Friday. Show all work for a full solution.

Extra CreditExtra Credit• In what polygon is the sum of the

measures of the exterior angles, one per vertex, equal to the sum of the measures of the angles of the polygon?

• Due Friday. Show all work for a full solution.

Extra CreditExtra Credit• In what polygon is the sum of the

measures of the exterior angles, one per vertex, equal to the sum of the measures of the angles of the polygon?

• Due Friday. Show all work for a full solution.

Extra CreditExtra Credit• In what polygon is the sum of the

measures of the exterior angles, one per vertex, equal to the sum of the measures of the angles of the polygon?

• Due Friday. Show all work for a full solution.

Extra CreditExtra Credit• In what polygon is the sum of the

measures of the exterior angles, one per vertex, equal to the sum of the measures of the angles of the polygon?

• Due Friday. Show all work for a full solution.