Exterior angles of polygons

Learning Objectives Define an exterior angle of a convex polygon. State and apply the Polygon Exterior Angle Sum Theorem. Calculate the measure of a single exterior angle of a regular polygon. Determine the number of sides of a regular polygon given the measure of one exterior angle. Solve for unknown variables in problems involving the exterior angles of irregular polygons. Prove the relationship between an interior angle and its corresponding exterior angle. Apply exterior angle properties to solve multi-step geometric problems. Ever wonder how a robot vacuum navigates a room's corners or how a stop sign gets its perfect shape? 🤖 It all comes down to the turns, or 'exterior angles'! In this tutorial, we will explore the angles formed on the outside of po...

TermDefinitionExample PolygonA closed, two-dimensional figure made up of three or more straight line segments (sides) that meet at points called vertices.A triangle, a square, a pentagon, and an octagon are all polygons. Exterior AngleAn angle formed by one side of a polygon and the extension of an adjacent side. It is outside the polygon.If you walk along the side of a square and then turn at the corner to walk along the next side, the angle of your turn is the exterior angle. Interior AngleAn angle on the inside of a polygon formed by two adjacent sides.The four angles inside a rectangle are all interior angles, each measuring 90°. Convex PolygonA polygon where all interior angles are less than 180°. All vertices point outwards, and any line segment connecting two vertices stays entirel...

Polygon Exterior Angle Sum Theorem \sum \text{Exterior Angles} = 360^\circ For any convex polygon, regardless of the number of sides, the sum of the measures of the exterior angles (one at each vertex) is always 360°. This is because walking around the perimeter of any polygon results in one full turn. Measure of One Exterior Angle of a Regular Polygon \text{Exterior Angle} = \frac{360^\circ}{n} For a regular polygon with 'n' sides, all exterior angles are equal. To find the measure of a single exterior angle, divide the total sum (360°) by the number of sides (or angles), n. Interior and Exterior Angle Relationship \text{Interior Angle} + \text{Exterior Angle} = 180^\circ At any single vertex of a convex polygon, the interior angle and its corresponding ex...