Triangles 3
Exterior Angles
Name __________________________
Activity
I. Discovering Exterior Angles of a Triangle
An exterior angle is an angle that is created when the side of a triangle is extended into the
exterior of the triangle.
2
1 3
1. Which of the angles in the figure are not
exterior angles of the triangle?
4
2. How many exterior angles does a triangle have
a) at one vertex?
6 5
9
8
7
b) altogether?
3. a) Is it possible that all of the triangle’s exterior angles of a triangle are equal? Explain.
b) Is it possible that all of the triangle’s exterior angles of a triangle are unequal? Explain.
II. Discovering the Triangle Exterior Angle Theorem (Remote Exterior Angle Theorem)
4. The sum of the interior angles of a triangle is _____________.
U
3
5. Given  CUP, identify:
a) an exterior angle
b) an interior angle adjacent to the exterior angle
C
2
1
4
P
c) 2 remote(meaning the two angles not adjacent to the exterior) interior angles
6. On patty paper, trace and label the above triangle CUP with 1, 2, 3, and 4.
7. Use a protractor to measure angles 2, 3, and 4. Label the angles on the patty paper.
8. What did you notice about 2, 3, and 4? Hint: add 2 and 3
9. Make a conjecture about the relationship between an exterior angle and its 2 remote interior
angles.
Find the values of all variables.
10.
11.
12.
61°
x°
39°
57
y°
x°
48°
110
(y + 10)
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Triangles 3
For problems 13-20, find x. Use your answers to work through the maze.
Start at S.
138
113°

115
24
28
45
157
120
20
17°
15°
83
10°
81
161
18
S
12°
13.
84
175
14.
x°
50°
15.
(7x)
(5x)°
(3x)°
34°
(3x)
(7x)°
(5x + 50)
x°
33°
16.
91°
151°
17.
90°
87°
54°
x°
18.
21°
134°
20.
x°
19.
x°
95°
148°
The ratio of angles of a triangle is 20:30:30. Find the measure of the smallest angle of the
triangle.
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Triangles 3
Triangle 3 Activity Key
1. 2, 5,  8
2. a) 2
b) 6
3. a) Yes, if the triangle is an equilateral triangle then all
exterior angles would measure 120º
because 180-60=120..
b) Yes, if all the interior angle measures in the triangle are
different then all of the exterior angle measures would
be different.
9. Conjecture: The measure of an exterior angle is equal
to the sum of the two remote interior angles.
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