Question

given: ∠1 and ∠2 are supplements,∠3 and ∠4 are supplements,and ∠1 ≅ ∠4.prove: ∠2 ≅ ∠3assemble the proof by dragging tiles tothe statements and reasons columns.tile options:statements/reasons tiles: given, substitution property, definition of ≅ angles, def. of supplementary angles

Explanation:

Step1: List given statements

$\angle 1$ and $\angle 2$ are supplements, $\angle 3$ and $\angle 4$ are supplements, $\angle 1 \cong \angle 4$

Step2: Use congruent angles definition

$m\angle 1 = m\angle 4$

Step3: Apply supplement definition

$m\angle 1 + m\angle 2 = 180^\circ$, $m\angle 3 + m\angle 4 = 180^\circ$

Step4: Substitute $\angle1$ for $\angle4$

$m\angle 1 + m\angle 2 = m\angle 3 + m\angle 1$

Step5: Simplify to prove congruence

$m\angle 2 = m\angle 3 \implies \angle 2 \cong \angle 3$

Answer:

Statements	Reasons
$m\angle 1 = m\angle 4$	definition of $\cong$ angles
$m\angle 1 + m\angle 2 = 180^\circ$, $m\angle 3 + m\angle 4 = 180^\circ$	def. of supplementary angles
$m\angle 1 + m\angle 2 = m\angle 3 + m\angle 1$	substitution property
$\angle 2 \cong \angle 3$	definition of $\cong$ angles