Question

1. △abc with db parallel to ac and cb extended to make ce
2. ∠a≅∠abd
3. ∠c≅∠dbc
4. m∠a = m∠abd; m∠c = m∠dbe
5. m∠abd + m∠dbe + m∠abc = 180°
6. m∠a + m∠c + m∠abc = 180°
7. m∠a + m∠abc + m∠c = 180°

(1 point)
statement 4 has a mistake. it should say ∠a≅∠dbe.
statement 5 has a mistake. it should say m∠abd + m∠dbe + m∠bca = 180°.
statement 3 has a mistake. it should say ∠c≅∠dbe.
statement 3 has a mistake. it should say ∠dbe≅∠a.

Explanation:

Step1: Analyze angle - congruence relationships

Given \(DB\parallel AC\), \(\angle A\) and \(\angle ABD\) are alternate - interior angles, and \(\angle C\) and \(\angle DBC\) are alternate - interior angles.

Step2: Check statement 4

By the definition of congruent angles, if \(\angle A\cong\angle ABD\) and \(\angle C\cong\angle DBE\) (from the parallel - line properties and angle - relationships), statement 4 is correct as written.

Step3: Check statement 5

Since \(\angle ABD+\angle DBE+\angle ABC\) form a straight - angle (\(\angle CBE\)), \(m\angle ABD + m\angle DBE+m\angle ABC = 180^{\circ}\), so statement 5 is correct.

Step4: Check statement 3

\(\angle C\) and \(\angle DBC\) are alternate - interior angles for \(DB\parallel AC\). \(\angle C\) is not congruent to \(\angle DBE\) based on the parallel - line and angle - relationship in the given triangle and parallel lines. The correct congruence for the parallel - line property is \(\angle C\cong\angle DBC\). So statement 3 has a mistake.

Answer:

Statement 3 has a mistake. It should say \(\angle C\cong\angle DBE\).