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statements reasons 1) \\(l \\parallel n\\) given 2) \\(m\\angle 3 + m\\…

Question

statements reasons

  1. \\(l \parallel n\\) given
  2. \\(m\angle 3 + m\angle 4 = 180^{\circ}\\)
  3. \\(m\angle \box + m\angle 5 = 180^{\circ}\\)
  4. \\(m\angle 3 + m\angle \box = m\angle 8 + m\angle 5\\)
  5. \\(\angle 4 \cong \angle 8\\)
  6. \\(m\angle \box = m\angle 8\\) definition of congruent angles
  7. \\(m\angle 3 + m\angle \box = m\angle 8 + m\angle 5\\)
  8. \\(m\angle 3 = m\angle 5\\) subtraction property of equality
  9. \\(\angle 3 \cong \angle 5\\) definition of congruent angles

Explanation:

Identificar la razón para la afirmación 2

$$ \text{Afirmación 2: } m\angle3 + m\angle4 = 180^\circ \implies \text{Linear Pair Postulate} $$

Identificar el ángulo faltante en la afirmación 3

$$ \text{Afirmación 3: } m\angle8 + m\angle5 = 180^\circ \implies \text{Ángulo faltante: } 8 $$

Identificar el ángulo faltante en la afirmación 4

$$ \text{Afirmación 4: } m\angle3 + m\angle4 = m\angle8 + m\angle5 \implies \text{Ángulo faltante: } 4 $$

Answer:

Question 1

  1. \(m\angle3 + m\angle4 = 180^\circ\) tiene como razón <blank>Linear Pair Postulate</blank>.
  1. \(m\angle\) <blank>8</blank> \(+ m\angle5 = 180^\circ\)
  1. \(m\angle3 + m\angle\) <blank>4</blank> \(= m\angle8 + m\angle5\)