Question

vertical angles complementary angles supplementary angles adjacent angles that are neither complementary nor supplementary

Explanation:

Step1: Define vertical angles

Vertical angles are opposite angles formed by two intersecting lines. In the diagram, \(\angle INJ\) and \(\angle MN L\) are vertical angles.

Step2: Define complementary angles

Complementary angles are two angles whose sum is \(90^{\circ}\). In the diagram, \(\angle KNJ\) and the right - angle part (if we consider the right - angle formed at \(N\) with some adjacent small angles) is not applicable here. Wait, no, looking at the lines, if we assume the right - angle is \(90^{\circ}\), but actually, vertical angles: \(\angle INJ\) and \(\angle MN L\) (opposite angles formed by intersecting lines \(IJ\) and \(ML\)). Complementary angles: \(\angle KNJ\) and \(\angle JNL\) (but no, wait, no. Wait, vertical angles: \(\angle INM\) and \(\angle JNL\) (opposite angles). Complementary angles: \(\angle KNJ\) and \(\angle KNL\) (sum to \(90^{\circ}\) as there is a right - angle symbol). Supplementary angles: \(\angle INJ\) and \(\angle JNL\) (sum to \(180^{\circ}\) as they form a linear pair). Adjacent angles that are neither complementary nor supplementary: \(\angle KNJ\) and \(\angle INJ\) (their sum is not \(90^{\circ}\) or \(180^{\circ}\)).

Answer:

vertical angles: \(\angle INM\) and \(\angle JNL\); complementary angles: \(\angle KNJ\) and \(\angle KNL\); supplementary angles: \(\angle INJ\) and \(\angle JNL\); adjacent angles that are neither complementary nor supplementary: \(\angle KNJ\) and \(\angle INJ\)