Question

which angle is supplementary to $\angle 5$? image of intersecting lines with angles labeled 1,2,3,4,5,6,7,8 options: $\angle 4$, $\angle 2$, $\angle 1$, $\angle 6$

Explanation:

Step1: Recall supplementary angles

Supplementary angles are two angles whose sum is \(180^\circ\) (a straight angle).

Step2: Analyze the diagram

In the diagram, \(\angle5\) and \(\angle6\) form a linear pair (they are adjacent and form a straight line). A linear pair of angles is supplementary, so \(\angle5 + \angle6=180^\circ\). Let's check the other options:

• \(\angle5\) and \(\angle4\): No, they don't form a linear pair or have a sum of \(180^\circ\).
• \(\angle5\) and \(\angle2\): No, they are not related in a way to sum to \(180^\circ\).
• \(\angle5\) and \(\angle1\): No, they are not related in a way to sum to \(180^\circ\).

Answer:

\(\angle6\)