Question

given: ∠1 and ∠2 are supplementary. prove: a || b. proof: it is given that ∠1 and ∠2 are supplementary. ∠1 and ∠3 are also supplementary, so ∠2≅∠3. since ____ are corresponding angles, a || b.

Explanation:

Step1: Recall supplementary - angle property

Given $\angle1+\angle2 = 180^{\circ}$ and $\angle1+\angle3=180^{\circ}$, by the property of supplementary angles, if $\angle1+\angle2=\angle1 + \angle3$, then $\angle2=\angle3$ (subtracting $\angle1$ from both sides).

Step2: Recall corresponding - angle property

Corresponding angles are equal when two lines are parallel. $\angle2$ and $\angle3$ are corresponding angles. If corresponding angles are equal, then the two lines $a$ and $b$ are parallel.

Answer:

$\angle2$ and $\angle3$