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3.2 Angles
Angles are measured in degrees using a protractor.
Degrees can be further
broken down into:
Minutes
Seconds
Angles of a Triangle
Pay close attention to the terminology being used. It will probably be new to many
of you. You need to understand and remember these new terms related to triangles
and how to use them.
Ray - Part of a line that has an endpoint at one end and continues infinitely far in
the opposite direction. It typically looks like this:
●
Angle - Symbolized by  . Angles are formed by two rays
which intersect at their end points.
1
The common endpoint in the figure is called the vertex.
Each of the rays is referred to as a side.
A is a point on one of the rays; C is a point on the other ray.
There are four ways to refer to the angle in the figure above.
1
B
ABC
CBA
(In the last two names, you must have the vertex in the middle.)
The symbol used for degrees is o. (It’s the same symbol you would use if you were
measuring temperature.) Examples of angles in terms of degrees:
Right turn ________
Spin out where you end up facing in the opposite direction _________
Spin out where you end up facing the same direction you started_________
Given that a complete rotation (full circle) is 360o, then 1o would be how much of a
complete rotation ________(fraction).
Given any triangle, the sum of the measures of all 3 angles equals 180o.
mA  mB  mC  180
Complementary Angles – two angles whose measures total 90o.
mABC  mCBD  mABD  90
ABC is the complement of CBD
CBD is the complement of ABC
A
C
B
D
Given angle “x,” how would you find its complement?
___________________________________________________________________
Supplementary Angles – two angles whose measures total 180o.
mABC  mCBD  mABD  180
ABC is the supplement of CBD
CBD is the supplement of ABC
A
Given angle “x,” how would you find its supplement?
C
B
D
Angle Facts:
1. Turning a complete circle is 360o
2. The angles in a triangle add up to 180o
3. A straight line is 180o
4. Parallel lines have equal angles
Study the following sets of lines carefully. You are going to see this same type of
configuration many more times, but it won’t be presented quite as clearly as you see
below.
Notice the parallel lines create two groups of angles that are all the same. All I
really need to tell you is one angle and you should be able to figure the rest.
Here is a cool website I recently found. Check it out. Some of
the terminology used may be a bit different than what we are
using, but all the concepts are the same. This should help you
practice with angles and lots of other stuff.
http://www.mathsisfun.com/geometry/index.html
How many angles are there in this figure?
Assign one _____________
What are the rest?
Figuring out the angles in a hexagon
Draw a regular hexagon with sides = 8 cm.
Find the angles in the trim around a regular hexagon window.
b
c
d
e
f
a
Calculate the angles in the trapezoid window and in
the trim around it. You may assume the bottom two
corners are right angles. You may assume the
outside trapezoid is proportional to the inside
trapezoid and the thickness of the frame is
consistent.
This is an Activity (worth 5 points) - Your time to draw (due at next class meeting) Use your protractor to make an
isometric drawing of a box 4 cm x 6 cm x 10 cm. Use a left angle of 25o and a right angle of 35o. An isometric drawing is
a 3D representation of an object where 3 of the sides are seen, all the vertical lines are parallel and all of the angles
consistent with the starting measures.
Homework: All of the problems in section 3.2.
Section 3.2:
1. A = 58o
B = 64o
C = 110o,
D = 71o
E = 141o
F = 152o
G = 118o
H = 134o
I = 39o
J = 28o
2. A = 43o
B = 58o
C = 64o
D = 285o
3. A = 125o
B = 21o
C = 35o
4. A = 124o
B = 56o
C = 68o
D = 68o
E = 112o
F = 124o
5. D = 72o
6. A = 118o
B = 62o
C = 118o
D = 118o
E = 152o
7.
Hole #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Angle
0°
24°
48°
72°
96°
120°
144°
168°
192°
216°
240°
264°
288°
312°
336°