Joe tried to prove that the sum of a triangle's interior angle measures is 180
°
180°180, degree

A
A
C
C
B
B
ℓ
ℓ
4
4
3
3
5
5
1
1
2
2
Statement Reason
1 Construct line
ℓ
ℓell through
C
CC parallel to
A
B
↔
AB
A, B, with, \overleftrightarrow, on top.
2
m
∠
4
=
m
∠
2
m∠4=m∠2m, angle, 4, equals, m, angle, 2 and
m
∠
1
=
m
∠
5
m∠1=m∠5m, angle, 1, equals, m, angle, 5 Alternate interior angles formed by parallel lines have equal measures.
3
m
∠
5
+
m
∠
4
+
m
∠
3
=
180
°
m∠5+m∠4+m∠3=180°m, angle, 5, plus, m, angle, 4, plus, m, angle, 3, equals, 180, degree Angles that combine to form a straight angle have measures that sum to
180
°
180°180, degree.
4
m
∠
1
+
m
∠
2
+
m
∠
3
=
180
°
m∠1+m∠2+m∠3=180°m, angle, 1, plus, m, angle, 2, plus, m, angle, 3, equals, 180, degree Substitution (2,3)
What was the first mistake in Joe's proof?
Choose 1
Choose 1

(Choice A)
A
Constructing a parallel line like this isn't necessarily possible.

(Choice B)
B
Angles
∠
4
∠4angle, 4 and
∠
2
∠2angle, 2 are not alternate interior angles, and neither are
∠
1
∠1angle, 1 and
∠
5
∠5angle, 5.

(Choice C)
C
Angles
∠
3
∠3angle, 3,
∠
4
∠4angle, 4, and
∠
5
∠5angle, 5 don't form a straight angle.

(Choice D)
D
The substitution isn't correct