Exterior Angles of Polygons

Exterior Angles of Polygons

Exterior angles are formed by extending one end of each polygon side.

X, Y, and Z are exterior angles and A, B, C, D, and E are exterior angles.

Exterior Angles of Polygons

On any polygon, regular or irregular, there is a relationship that exists among exterior angles. On any polygon, the exterior angles will always

add up to 360 degrees.

Exterior Angles of Polygons Mini-Lab

Remember, an angle and its adjacent exterior angle form a straight line or a straight angle. The

two angles’ sum is 180 degrees.

Exterior Angles of Polygons Mini-Lab

To find the size of an exterior angle, subtract the interior angle size from 180 degrees.

Adding up all exterior angles (110 + 130 + 120), we find that the sum of the exterior angles is

360 degrees!

Exterior Angles of Polygons Mini-Lab

Expand your thoughts… You know that a straight angle = 180 degrees, and you know that the

interior angles of all triangles sum to 180 degrees.

It stands to reason then, that an exterior angle equals the sum of the remote (or opposite)

angles.

120

6060

60

Exterior Angles of Polygons Mini-Lab

Find the value of x and then find the measure of the missing angle. Be prepared to discuss how

you got each measure:

2x + 10

125

2x + 10 = 25 + 1252x + 10 = 1502x = 140X = 70

The exterior angle measure is2(70) + 10 which equals 150 degrees.

This means the missing interior angle is 180 – 150 or 30 degrees!

If this is correct, the sum of interior angles should equal 180 degrees as well. 30 + 25 + 125 = 180!

Practice Time!

Exterior Angles of Polygons Checkpoint

Find the size of each exterior angle on a regular pentagon

X + 108 = 180 - 108 -108

X = 72

Exterior Angles of Polygons Checkpoint

How many sides does a regular polygon have if one of its exterior angles measures 45 degrees?

HINT: Think about the sum of exterior angles and the definition of a REGULAR polygon!

45n = 360 n = 8

Exterior Angles of Polygons Checkpoint

Try it again…How many sides does a regular

polygon have if each exterior angle is 30 degrees?

30n = 360

n = 12

Exterior Angles of Polygons Small Group Challenge

Find the value of x and then find the measure of the missing angle. Be prepared to discuss how

you got each measure:

78

4x - 10

X + 32

4x – 10 = 78 + x + 324x – 10 = x + 1104x = x + 1203x = 120x = 40

Check….4(40) – 10 = 150

180 – 150 = 30

AND

78 + (40 + 32) = 15078 + 72 = 150

180 - 150 = 30

The missing angle is 30 degrees!

Homework

• Exterior Angle Theorem Worksheet (both sides)

• DUE TOMORROW!