Download Exterior Angle Theorem Date: ______ Pd: ____ H

Geometry – Unit 5 Practice
Exterior Angle Theorem
Name: _____________________________!
Date: ___________ Pd: ____
G.CO.C.10
Quick Concept: An exterior angle is formed between a side and the
extension of a side. It will always be a linear pair with an internal angle. In
the diagram below, ∠4 is the exterior angle. The exterior angle theorem
states that the EXTERNAL ANGLE IS EQUAL TO THE SUM OF THE TWO
REMOTE ANGLES. The remote angles are those interior angles that are not
adjacent to the exterior angle so in this case ∠1 & ∠2 are the remote angles.
B
1
4
3
2
C
A
1) Activity – Draw a triangle. Extend one of its sides to form an external
angle. Cut out the triangle and the external angle. Tear off the two
remote angles and place them in the external angle - what do you
notice?
2) Jeff is trying to prove that sum of the remote angles is equal to the

external angle. He begins by translating ∆ABC by vector AC placing
B
1
∠2 ≅ ∠B’CC’ in the interior of the external angle. AB || CB ' because
translations form parallel lines. ∠3 ≅ ∠3 because of the reflexive
property.
C
A
B'
B
How would he complete this proof?
4
3
2
1
2
2
3
3) Megan is trying to prove that the sum of the remote angles is equal to the
external angle. She begins by stating that:
B
m∠1 + m∠2 + m∠3 = 180 because the interior angles of a ∆ = 180°.
m∠3 + m∠4 = 180° because linear pairs are supplementary.
How would she complete this proof?
SNRPDP
Unit 5: Triangles and Triangle Congruence
NVACS – Revised 2015-2016
C'
C
A
1
2
A
4
3
C
Page 1 of 2
Practice – Unit 5 (cont.)
4) Find the value of x.
a)
b)
c)
x
96°
x
x
23°
56°
44°
111°
142°
x = _____________
x = _____________
x = _____________
d)
e)
f)
x
31°
x
57°
128°
52°
x
x = _____________
5) Find the value of x.
a)
x = _____________
b)
73°
x = _____________
c)
78°
56°
x
136°
x
x
26°
x = _____________
x = _____________
d)
x = _____________
e)
2x - 5
51°
3x - 1
145°
x
x = _____________
x = _____________
Page 2 of 2
x