Question

which angles in the picture are not supplementary? options: 1 and 2, 2 and 3; 1 and 3, 2 and 4; 4 and 1, 3 and 4; 2 and 3, 1 and 4

Explanation:

Step1: Recall supplementary angles

Supplementary angles sum to \(180^\circ\). Vertical angles are equal and non - supplementary (unless they are \(90^\circ\), but here with two intersecting lines, vertical angles are equal and their sum is \(2\theta\) where \(\theta\) is the angle measure, not \(180^\circ\) unless \(\theta = 90^\circ\), but in general, vertical angles are not supplementary.

Step2: Identify vertical angles

In the diagram with two intersecting lines, \(\angle1\) and \(\angle3\) are vertical angles, \(\angle2\) and \(\angle4\) are vertical angles. Angles that form a linear pair are supplementary (sum to \(180^\circ\)). For example, \(\angle1\) and \(\angle2\), \(\angle2\) and \(\angle3\), \(\angle3\) and \(\angle4\), \(\angle4\) and \(\angle1\) are linear pairs (supplementary). The pairs that are not supplementary are the vertical angle pairs: \(\angle1\) and \(\angle3\), \(\angle2\) and \(\angle4\). Looking at the options, the option "1 and 3; 2 and 4" is the one where the angles are not supplementary.

Answer:

1 and 3; 2 and 4 (the third option in the list of choices)