Question

in the diagram, two parallel lines are cut by a trans
which angles are supplementary to ∠4?
choose all that apply.
∠1 ∠2 ∠3 ∠5
∠6 ∠7 ∠8

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze adjacent angles

\(\angle3\) and \(\angle4\) form a linear pair. So, \(\angle3+\angle4 = 180^{\circ}\).

Step3: Use properties of parallel lines and transversal

Since the two lines are parallel, \(\angle5\) and \(\angle4\) are same - side interior angles. So, \(\angle5+\angle4=180^{\circ}\).
\(\angle6\) and \(\angle4\) are alternate interior angles. But \(\angle6\) is not supplementary to \(\angle4\) directly. However, \(\angle6\) and \(\angle5\) are supplementary (\(\angle5+\angle6 = 180^{\circ}\)), and since \(\angle5+\angle4=180^{\circ}\), we can also note that \(\angle6\) is not supplementary. But \(\angle3\) (adjacent) and \(\angle5\) (same - side interior) are supplementary to \(\angle4\). Also, \(\angle1\) and \(\angle3\) are vertical angles (\(\angle1=\angle3\)), so \(\angle1+\angle4 = 180^{\circ}\) (because \(\angle3+\angle4 = 180^{\circ}\)).

Answer:

\(\angle1\), \(\angle3\), \(\angle5\)