Apply angle relationships at intersections and with parallel lines cut by a transversal, including vertical, corresponding, alternate, and same-side interior angles, linear pairs, perpendicular lines, and simple equations for unknown measures. Use triangle and quadrilateral properties, including angle sums, exterior-angle relationships, side and diagonal relationships, and specialized properties of rectangles, rhombi, squares, parallelograms, and isosceles trapezoids. Apply interior- and exterior-angle sums to convex polygons, find angles of regular polygons, and justify unknown-angle solutions from marked diagrams using symbolic and written geometric reasoning rather than visual appearance.