Math 8 (Period 1)

Polygons and Angles 5-4

Polygon: A closed figure with three or more line segments ( no overlapping lines)

Some common polygons: triangle, quadrilateral, pentagon hexagon, octagon

Interior Angle Sum Formula: (n - 2)180   where n is the number of sides of the polygon
Working from this formula
A triangle has 180 degrees (n - 2)180 in this case is (3 - 2)180 = 1(180) = 180 degrees
( A triangle has 3 sides…)

A quadrilateral has 360 degrees ( 4 - 2)180 = 2(180)= 360 degrees
(A quadrilateral has 4 sides—in fact quad means 4 and lateral means sides)

A pentagon has 540 degrees ( 5 - 2)180 = 3(180) = 540 degrees
and so on…

Regular polygon: All sides and angles are congruent
Equiangular means equal angles
An equilateral triangle is regular (notice the word lateral in equilateral)
A square is a regular quadrilateral

Once you find the TOTAL of all the interior angles of a polygon, if it is REGULAR, just divide the sum by the number of angles in the polygon and you will find the measurement of each angle.

Example: Find the measurement of each angle of a REGULAR hexagon.
A hexagon has 6 sides so (6-2)180 = 4(180) = 720  degrees for all the angles in a hexagon. Because it is REGULAR all the angles have the same measurement so divide 720 by 6
720/6 =  120.    Each angle is 120 degrees.

Exterior Angle Sum; It’s 360 degrees for ANY POLYGON!!!