How to calculate the measure of an inscribed angle.
How to prove that an angle inscribed in a semicircle is a right angle; how to solve for arcs and angles formed by a chord drawn to a point of tangency.
How to define circumscribed and inscribed circles and polygons relative to each other.
How to define an angle of elevation or an angle of depression.
How to identify supplementary and complementary angles.
How to define exterior angles and their remote interior angles and how to prove their properties.
How to define corresponding angles and their special properties.
How to label an angle bisector; how to use an angle bisector to find a missing variable.
How to duplicate an angle using a compass and straightedge.
How to find the sum of the exterior angles in a polygon and find the measure of one exterior angle in an equiangular polygon.
How to define alternate interior angles and their special properties.
How to define alternate exterior angles and their special properties.
How to apply the triangle angle sum theorem.
How to label an angle and how to differentiate between acute, right, obtuse, and straight angles.
How to derive the formula to find the sum of angles in any polygon.
How to define adjacent angles.
How to determine the relationship between the side inequalities and angle inequalities in a triangle.
How to define and identify vertical angles.
How to relate the sides of an angle bisected and the lengths of the opposite side.
How to prove that opposite angles in a cyclic quadrilateral are congruent; how to prove that parallel lines create congruent arcs in a circle.