Question

what is an angle that is supplementary to ∠hod?

Explanation:

Step1: Recall supplementary - angle definition

Two angles are supplementary if their sum is 180 degrees. If we assume that the angles are formed by intersecting lines and we know the properties of linear - pairs of angles. A linear - pair of angles is supplementary. If \(\angle HOD\) is given, an angle that forms a linear - pair with \(\angle HOD\) is supplementary to it.
Let's assume that the lines intersect at a point. If \(\angle HOD\) is one of the angles, then the angle adjacent to it and forming a straight - line with it is supplementary. For example, if \(\angle HOD\) and \(\angle DOG\) form a straight - line (a linear - pair), then \(\angle DOG\) is supplementary to \(\angle HOD\) since \(\angle HOD+\angle DOG = 180^{\circ}\).

Answer:

An angle that forms a linear - pair with \(\angle HOD\) (such as an adjacent angle sharing a common side and a common vertex with \(\angle HOD\) and whose non - common sides form a straight line with the non - common side of \(\angle HOD\))