Question

without using a protractor, can you tell if any of the angles are supplementary? choose the best explanation.
yes. ∠1 and ∠2 combine to form a straight angle with a measure of 180°.
yes. ∠1 and ∠7 are on the same side of the transversal, so they must be supplementary.
no. there is no way to tell if any angles are supplementary.

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\).

Step2: Analyze \(\angle1\) and \(\angle2\)

\(\angle1\) and \(\angle2\) form a linear - pair (they are adjacent and their non - common sides form a straight line). By the linear - pair postulate, if two angles form a linear pair, then they are supplementary. A linear pair of angles combines to form a straight angle (\(180^{\circ}\)).

Step3: Analyze \(\angle1\) and \(\angle7\)

\(\angle1\) and \(\angle7\) are not adjacent in a way that forms a linear pair. Just because they are on the same side of a transversal does not make them supplementary. There is no geometric postulate or theorem that states that two angles on the same side of a transversal (in a non - parallel line context, since we have no information about parallel lines) are supplementary.

Answer:

Yes. \(\angle1\) and \(\angle2\) combine to form a straight angle with a measure of \(180^{\circ}\).