Question

writing proofs write a two - column proof. 23. given m∠3 = 120°, ∠1 ≅ ∠4, ∠3 ≅ ∠4 prove m∠1 = 120° plan for proof first show that ∠1 ≅ ∠3. then use transitivity to show that m∠1 = 120°.

Explanation:

Step1: Given equal - angle relations

We know that $\angle1\cong\angle4$ and $\angle3\cong\angle4$.

Step2: Use transitive property of congruence

By the transitive property of congruence (if $a\cong b$ and $b\cong c$, then $a\cong c$), since $\angle1\cong\angle4$ and $\angle3\cong\angle4$, we can conclude that $\angle1\cong\angle3$.

Step3: Use measure of $\angle3$

Given that $m\angle3 = 120^{\circ}$. Since $\angle1\cong\angle3$, congruent angles have equal measures. So $m\angle1=120^{\circ}$.

Answer:

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