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2.4 Angle Properties in Polygons (Solutions).notebook December 02, 2015
2.4 Angle Properties in Polygons
In a CONVEX POLYGON, NO line segment that joins any 2 vertices of the polygon extends outside the polygon.
convex pentagon
A REGULAR POLYGON has all EQUAL sides & all EQUAL angles.
A POLYGON is a CLOSED figure made up of 3 or more line segments.
regular quadrilateral
irregular quadrilateral
irregular quadrilateral
concavepentagon
2.4 Angle Properties in Polygons (Solutions).notebook December 02, 2015
To find the sum of the measures of the INTERIOR angles of any polygon, use
To find the measure of each INTERIOR angle in a regular polygon, use
When there is only one exterior angle per vertex, the sum of the EXTERIOR angles of any CONVEX polygon is 360o.
To find the measure of any EXTERIOR angle for a REGULAR CONVEX POLYGON, the formula is:
1. The sum of the interior angles in a regular polygon is 1800o.
a) How many sides does this polygon have?
b) What is the measure of each of the interior angles?
2.4 Angle Properties in Polygons (Solutions).notebook December 02, 2015
3. Find the measure of each Exterior Angle of a regular dodecagon (12-sided).
b. 30 sides.
2. Find the sum of the measures of the interior angles of a polygon with...
a. 25 sides.
5. Determine the value of x in the diagram below.Then find the measure of each indicated angle.
2.4 Angle Properties in Polygons (Solutions).notebook December 02, 2015
6. Find the measures of all angles.
A
B
C
D
E
p.99
#1 ‐ 3, 7, 10, 11, 13, 16
2.4 Angle Properties in Polygons (Solutions).notebook December 02, 2015
ACTIVITY 1: Draw each polygon. Divide it into triangles by drawing diagonals from ONE vertex to all NON-ADJACENT vertices.
Draw at least the first 4 figures to see the pattern.
Polygon # of Sides # of Triangles FormedSum of
Interior Angles
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
n - gon
Make conjecture be made about the sum of Interior Angles of any polygon.Conjecture:
3. 4. 5. 6.
7. 8. 9. 10.
2.4 Angle Properties in Polygons (Solutions).notebook December 02, 2015
ACTIVITY 2: Draw the regular polygons indicated (at least the 1st 4) with only 1 exterior angle per vertex. Fill in the table below.
Polygon Sum of Interior Angles
Size of each Interior Angle
Size of each Exterior Angle
Sum of Exterior Angles
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
N - gon
Make a conjecture for the sum of the Exterior Angles of a regular convex polygon.
Conjecture:
3. 4.5.
6. 7.
0
18010
17020
16030
15040
140
50
130
60
120
70
110
80
100
90
90
27°
100
80
110
70
120
60
13050
14040
15030
16020
17010
180
0
