consider the following proof of the triangle angle sum theorem. which statement has a mistake?
given: $ \triangle a b c $ with $ \overleftrightarrow { d e } \parallel \overline { a c } $
prove: $ m \angle a + m \angle a b c + m \angle c = 180 ^ { \circ } $
identify total number of mistakes in the steps to prove that the sum of all the angles of a triangle is $ 180 ^ { \circ } $
| statements | reasons |
| --- | --- |
| 1 $ \triangle a b c $ with $ \overleftrightarrow { d e } \parallel \overline { a c } $ | 1 given |
| 2 $ \angle d b a \cong \angle a , \angle e b c \cong \angle c $ | 2 $ \overleftrightarrow { d e } \parallel \overline { a c } $ and alternate interior angles are congruent when lines are parallel |
| 3 $ m \angle d b a = m \angle a , m \angle e b c = m \angle c $ | 3 definition of congruent angles |
| 4 $ m \angle d b a + m \angle a b c + m \angle a c b = 180 ^ { \circ } $ | 4 definition of a straight angle |
| 5 $ m \angle a + m \angle a b c + m \angle c = 180 ^ { \circ } $ | 5 substitution |
(1 point)
statement $ \square $ has a mistake

Question

Accepted Answer

# Answer:
Statement 4 has a mistake.
# Explanation:
## Step1: Analyze statement 4
The sum of angles on a straight line is $180^{\circ}$. The angles on the straight line $DE$ at point $B$ are $\angle DBA+\angle ABC+\angle EBC = 180^{\circ}$, not $\angle DBA+\angle ABC+\angle ACB = 180^{\circ}$.

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QUESTION IMAGE

Question

Explanation:

Step1: Analyze statement 4

Answer:

statements	reasons
2 \\( \angle d b a \cong \angle a , \angle e b c \cong \angle c \\)	2 \\( \overleftrightarrow { d e } \parallel \overline { a c } \\) and alternate interior angles are congruent when lines are parallel
3 \\( m \angle d b a = m \angle a , m \angle e b c = m \angle c \\)	3 definition of congruent angles
4 \\( m \angle d b a + m \angle a b c + m \angle a c b = 180 ^ { \circ } \\)	4 definition of a straight angle
5 \\( m \angle a + m \angle a b c + m \angle c = 180 ^ { \circ } \\)	5 substitution