Interior and exterior angles of polygons (Review)

Learning Objectives Calculate the sum of the interior angles of any convex polygon. Determine the measure of a single interior angle and a single exterior angle of a regular polygon. Apply the property that the sum of the exterior angles of any convex polygon is 360°. Solve for unknown variables in algebraic expressions representing the angles of a polygon. Determine the number of sides of a regular polygon given the measure of one of its interior or exterior angles. Relate the measure of an interior angle and its corresponding exterior angle as a linear pair. Ever wondered why a beehive is made of perfect hexagons or why a stop sign has eight sides? 🛑 The geometry of their angles is the secret! This tutorial is a comprehensive review of the properties of interior and exte...

TermDefinitionExample PolygonA closed two-dimensional figure made up of three or more straight line segments connected end-to-end.A triangle (3 sides), a quadrilateral (4 sides), a pentagon (5 sides). Convex PolygonA polygon where all interior angles are less than 180°. If you extend any side, the line will not pass through the interior of the polygon.A standard rectangle or a regular hexagon. A star shape is non-convex (concave). Regular PolygonA polygon that is both equiangular (all angles are equal in measure) and equilateral (all sides are equal in length).An equilateral triangle or a square. Interior AngleAn angle formed by two adjacent sides inside a polygon.In a square, each of the four interior angles measures 90°. Exterior AngleAn angle formed by one side of a polygon and the ext...

Polygon Interior Angle Sum Theorem S = (n - 2) \times 180^{\circ} Use this formula to find the sum (S) of the measures of the interior angles of any convex n-gon, where 'n' is the number of sides. Interior Angle of a Regular Polygon A = \frac{(n - 2) \times 180^{\circ}}{n} Use this formula to find the measure of a single interior angle (A) of a regular n-gon. This only works for regular polygons where all angles are equal. Polygon Exterior Angle Sum Theorem S_{ext} = 360^{\circ} The sum of the measures of the exterior angles (one at each vertex) of any convex polygon is always 360°, regardless of the number of sides. Exterior Angle of a Regular Polygon E = \frac{360^{\circ}}{n} Use this formula to find the measure of a single exterior angle (E) of a...