Geometric Reasoning with Parallel Lines and Polygons (Combined)

Task goals

• Identify and name angle pairs formed at a point, on a straight line, and by a transversal crossing parallel lines (vertically opposite, alternate, corresponding, co-interior).
• Calculate an unknown angle using parallel-line angle relationships, stating the correct geometric reason (e.g. "alternate angles are equal").
• Calculate an unknown angle using the angle sum of a triangle or quadrilateral, or the exterior angle of a triangle, stating the reason used.
• Calculate the sum of interior angles, or a single interior or exterior angle, of a regular or irregular polygon.
• Combine parallel-line, triangle, quadrilateral and polygon angle-sum properties to solve a multi-step problem, constructing a short chain of fully justified reasoning.