Exterior Angles of Polygons Exterior Angles of Polygons

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 -Lab Mini 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 -Lab Mini 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 -Lab Mini 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. 120 60 60 60 It stands to reason then, that an exterior angle equals the sum of the remote (or opposite) angles.

Exterior Angles of Polygons -Lab Mini Find the value of x and then find the measure of the missing angle. Be prepared to discuss how you got each measure: 2 x + 10 = 25 + 125 2 x + 10 = 150 2 x = 140 X = 70 2 x + 10 The exterior angle measure is 2(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! 125

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! 45 n = 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? 30 n = 360 n = 12

Exterior Angles of Polygons Group Challenge Small Find the value of x and then find the measure of the missing angle. Be prepared to discuss how you got each measure: Check…. 4(40) – 10 = 150 4 x – 10 = 78 + x + 32 4 x – 10 = x + 110 4 x = x + 120 3 x = 120 x = 40 180 – 150 = 30 4 x - 10 AND 78 + (40 + 32) = 150 78 + 72 = 150 78 X + 32 180 - 150 = 30 The missing angle is 30 degrees!

Homework • Exterior Angle Theorem Worksheet sides) • DUE TOMORROW! (both