Regular/irregular polygon

Task goals

• State whether a described or pictured polygon is regular or irregular, and complete the statement that a regular polygon has all sides the same length and all interior angles equal.
• Find the sum of the interior angles of a polygon using 180(n - 2), for shapes from a triangle up to an octagon.
• Find the size of one interior angle of a regular polygon (pentagon, hexagon, octagon, nonagon, or decagon) by dividing the interior-angle sum by the number of sides.
• Find a missing interior angle of an irregular polygon given all its other interior angles.
• Find the number of sides of a polygon given its interior-angle sum, or given the size of one interior angle of a regular polygon.
• Justify why a polygon with equal sides and equal angles must be regular, and evaluate a claim that equal angles alone are enough to make a polygon regular.
• Find the missing angles of an irregular polygon whose interior angles are given as a ratio.
• Write a general formula relating a regular polygon's interior-angle sum to one interior angle and the number of sides, and use it to solve multi-step problems relating one regular polygon to another.