Exterior Angles of Polygons. Exterior angles are formed by extending one end of each polygon side....
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Transcript of Exterior Angles of Polygons. Exterior angles are formed by extending one end of each polygon side....
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!
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!