NYSTCE 222 – Childhood Mathematics (Grade 1-6) Practice Exam

To determine which geometric figure must always have an angle, it's important to understand the characteristics of each option.

An intersecting line is essential because it involves two lines crossing each other, and this intersection creates angles. Angles are formed when two rays share a common endpoint, called the vertex. In the case of intersecting lines, each point where the lines cross forms an angle, and therefore, this figure inherently involves angles.

A line segment, on the other hand, is simply a part of a line that has two endpoints, and it does not encompass any angles by itself. Similarly, a vertex is a point where two lines or line segments meet, but by itself, it doesn't constitute a geometric figure with an angle. Lastly, a transversal refers to a line that crosses two or more other lines, and while it can create angles with these lines, it is not a figure that must always have an angle by itself.

Therefore, the intersecting line is correctly identified as the figure that must always include angles due to the nature of its definition, where two lines meet and form distinct angles.