Question

1. given - m∠3 = 120°, ∠1 ≅ ∠4, ∠3 ≅ ∠4. prove - m∠1 = 120°. statements: m∠3 = 120°, ∠1 ≅ ∠4, ∠3 ≅ ∠4. reasons: 1. given

Explanation:

Step1: Recall congruent - angle property

If $\angle3\cong\angle4$, then $m\angle3 = m\angle4$. Since $m\angle3 = 120^{\circ}$, so $m\angle4=120^{\circ}$.

Step2: Use the given congruence

Given $\angle1\cong\angle4$. By the definition of congruent angles, if two angles are congruent, they have equal measures. So if $m\angle4 = 120^{\circ}$, then $m\angle1=120^{\circ}$.

Answer:

$m\angle1 = 120^{\circ}$