Question

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 the relationship between \(\angle4\) and other angles

• \(\angle4\) and \(\angle1\): They form a linear pair (adjacent angles on a straight line), so \(\angle4+\angle1 = 180^{\circ}\).
• \(\angle4\) and \(\angle3\): They form a linear pair (adjacent angles on a straight line), so \(\angle4+\angle3=180^{\circ}\).
• \(\angle4\) and \(\angle5\): \(\angle4\) and \(\angle5\) are related by the property of parallel - line transversal (if we assume the lines are parallel). Alternate interior angles and linear - pair concepts. \(\angle4\) and \(\angle5\) can be shown to be supplementary.

Answer:

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