Question

congruent supplements theorem linear pair theorem given definition of supplementary angles transitive property of congruence m∠1 = 110° ∠1 is supplementary to ∠2 ∠1 ≅ ∠3 m∠2 = 70° ∠2 is supplementary to ∠3 reset next

Explanation:

Step1: Match given values

$m\angle1=110^\circ$, $m\angle2=70^\circ$ → given

Step2: Verify supplementary angles

$m\angle1 + m\angle2 = 110^\circ+70^\circ=180^\circ$ → definition of supplementary angles
$m\angle2 + m\angle3 = 180^\circ$ (implied) → definition of supplementary angles

Step3: Apply congruent supplements theorem

If two angles are supplementary to the same angle, they are congruent → $\angle1\cong\angle3$

Answer:

1. $m\angle1 = 110^\circ$ and $m\angle2 = 70^\circ$: $\boldsymbol{given}$
2. $\angle1$ is supplementary to $\angle2$: $\boldsymbol{definition\ of\ supplementary\ angles}$
3. $\angle2$ is supplementary to $\angle3$: $\boldsymbol{definition\ of\ supplementary\ angles}$ (or $\boldsymbol{linear\ pair\ theorem}$ if $\angle2$ and $\angle3$ form a linear pair)
4. $\angle1\cong\angle3$: $\boldsymbol{congruent\ supplements\ theorem}$