Download (D3) Exterior Angles Activity

Triangles 3
Exterior Angles
Name __________________________
Date _______________ Period _______
Activity
I. Discovering Exterior Angles of a Triangle
The sides of the acute triangle at the right have been
extended to form its exterior angles.
1. Which of the numbered angles in the figure are not
exterior angles of the triangle?
1
3
4
2. How many exterior angles does a triangle have
a) at one vertex?
2
6 5
9
8
b) altogether?
7
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 interior angles
6. On patty paper, trace and label the above triangle CUP with 1, 2, 3, and 4.
7. Tear off 2 and 3. Place them inside 4 so that the vertices all match up and 2 and 3 do
not overlap.
8. What did you notice about 2, 3, and 4?
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
10
12
84
175
S
13.
14.
x°
50°
(3x)°
x°
134°
(7x)
(3x)
(7x)°
17.
33°
(5x + 50)
90°
87°
91°
21°
15.
(5x)°
34°
16.
20.
81
161
18
18.
83
151°
x°
x°
54°
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.
b) Yes, if all the interior angle measures in the triangle are
different then all of the exterior angle measures would
be different.
4. 180º
5. a) 4
b)  1
c) 2, 3
8. 2 and 3 fit perfectly into 4
9. The exterior angle of a triangle equals the sum of the two
remote interior angles.
10. x = 100
11. x = 42, y = 28
12. y = 117
13. 84
14. 12
15. 10
16. 120
17. 24
18. 113
19. 138
20. 45º
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