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Name of Lecturer: Mr. J.Agius
Course: HVAC1
Lesson 49
Chapter 9: Angles and Shapes
Polygons
A polygon is a plane shape with straight sides.
Is it a Polygon?
Polygons are 2-dimensional shapes. They are made of straight lines, and
the shape is "closed" (all the lines connect up).
Polygon
(straight sides)
Polygon comes
"angle".
from
Not a Polygon
(has a curve)
Not a Polygon
(open, not closed)
Greek. Poly- means
"many"
and -gon means
Types of Polygons
Simple or Complex
A simple polygon has only one boundary, and it doesn't cross over itself.
A complex polygon intersects itself!
Simple Polygon
(this one's a Pentagon)
Complex Polygon
(also a Pentagon)
Concave or Convex
A convex polygon has no angles pointing inwards. More precisely, no
internal angles can be more than 180°.
9 Angles & Shapes
Page 1
Name of Lecturer: Mr. J.Agius
Course: HVAC1
If there are any internal angles greater than 180° then it is concave.
(Think: concave has a "cave" in it)
Convex
Concave
Regular or Irregular
If all angles are equal and all sides are equal, then it is regular,
otherwise it is irregular
Regular
Irregular
More Examples
Complex Polygon
(a "star polygon", in
this case, a pentagram)
9 Angles & Shapes
Concave Octagon
Irregular Hexagon
Page 2
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Names of Polygons
If it is a Regular Polygon...
Name
Sides
Shape
Interior Angle
Triangle (or Trigon)
3
60°
Quadrilateral (or Tetragon)
4
90°
Pentagon
5
108°
Hexagon
6
120°
Heptagon (or Septagon)
7
128.571°
Octagon
8
135°
Nonagon (or Enneagon)
9
140°
Decagon
10
144°
Hendecagon (or Undecagon)
11
147.273°
Dodecagon
12
150°
n-gon
n
(n-2) × 180° / n
These notes were taken from the following website address.
http://www.mathsisfun.com/geometry/polygons.html
9 Angles & Shapes
Page 3
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Exterior Angles of Polygons
The Exterior Angle is the angle between any side of a shape,
and a line extended from the next side.
Note: If you add up the Interior Angle and Exterior Angle you get a
straight line, 180°. (See Supplementary Angles)
Polygons
A Polygon is any flat shape with straight sides
The Exterior Angles of a Polygon add up to 360°
For more information, go to the following site.
http://www.mathopenref.com/polygonexteriorangles.html
9 Angles & Shapes
Page 4
Name of Lecturer: Mr. J.Agius
Course: HVAC1
Exercise 1:
Choose the correct answer from the choices listed.
1. How many degrees are there in the sum of the exterior angles of a dodecagon ?
4320°
2160°
1800°
360°
2. Find the number of degrees in each exterior angle of a regular pentagon.
36°
72°
108°
360°
3. If each exterior angle of a regular polygon contains 40º, how many sides does the
polygon have ?
9
10
11
12
4. What is the measure of one exterior angle of a regular decagon ?
36°
72°
108°
360°
5. What is the sum of the exterior angles of a polygon with 36 sides ?
10°
360°
36°
12960°
9 Angles & Shapes
Page 5
Name of Lecturer: Mr. J.Agius
Course: HVAC1
is the measure of each exterior angle of a stop sign?
6. What
(A stop sign is a "regular" geometric figure.)
36°
45°
48°
120°
Exercise 2:
In each question find the angle marked xo.
1.
2.
85o
70o
150o
45o
xo
xo
3.
4.
58
xo
o
xo
80o
50o
62o
72o
xo
o
x
9 Angles & Shapes
76o
Page 6