**TI89**MAINAppVariable file 01/06/05, 18:21Rgeometrys¥ZTheorem 10.1: Finding the sum of ALL interior angles
VOCABULARY:
regular polygon- A perfect figure.
Theorem 10.1: The sum of the measures of angles in a n-gon is expressed with the equation of (n-2)*180.
Examples:
TRIANGLE 3-gon:
Sides: 3
Sum of ALL the Interior Angles: 1(180)=180
QUADRILATERAL:
Sides: 4
Sum "":2(180)=360
UNKNOWN N-GON:
Sides: (n-2)
Sum "": (n-2)180
148-gon:
Sides: 148
Sum"": (148-2)*180=146(180)=26280
Corollary to Theorem 10.1:Finding the measure of oneinterior angle.
Corollary 10.1: The measure of an interior angle of a regular n-gon is the sum of all the angles divided by the number of sides.
VOCABULARY:
regular- all angles of an n-gon are exactly the same
"n-gon"- a polygon with 'n' as a variable.
FORMULAS:
Formula for Corollary: ((n-2)180)/n, having 'n' the number of sides of the polygon. Theorem 10.1/2 and Corollary to Theorem 10.1/2
Theorem 10.1/2: The sum of the exterior angles, one at each vertex is 360 degrees.
Corollary: The measure of an exterior angle of a n-gon is 360 degrees divided by the number of sides.
So the sum of one exterior angle is 360 divided by the number of sides. If you know one interior angle, then you know on exterior, vice versa, because of one side form a strait angle and inevitably equal 180 degrees!
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