A vertex angle refers to the angle that is formed by the two lines crossing at a vertex. When asked for a vertex angle, the intended query is typically for the size of the angle in degrees or radians.
A vertex is the result of two non-perpendicular lines intersecting, often forming a corner of a shape. For example, a square has four vertices due to having four sides and four corners. The angle of a vertex is measured on the inside of the shape. For a square, the angle would be measured between two connected sides, which would always be 90 degrees.