Interior angles of polygons

Learning Objectives Identify and classify polygons based on their number of sides. Define and identify interior angles of polygons. Derive the formula for the sum of the interior angles of any convex polygon. Calculate the sum of the interior angles for a given polygon. Determine the measure of one interior angle of a regular polygon. Solve for unknown interior angles in polygons using algebraic equations. Have you ever wondered how architects design buildings with perfectly straight walls and precise corners? 📐 It all comes down to understanding the angles inside shapes! In this lesson, you'll discover the fascinating world of polygons and their interior angles. You'll learn how to calculate the sum of these angles and even find individual angle measures, which...

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). Vertex (plural: Vertices)A point where two sides of a polygon meet. These are the 'corners' of the polygon.In a square, there are four vertices, one at each corner. SideA straight line segment that forms part of the boundary of a polygon.A triangle has 3 sides, a hexagon has 6 sides. Interior AngleAn angle formed inside a polygon at one of its vertices by two adjacent sides.In a square, each interior angle is 90 degrees. Regular PolygonA polygon where all sides are of equal length and all interior angles are of equal measure.An equilateral triangle, a square, a regular pentagon. Co...

Sum of Interior Angles of a Polygon $S = (n-2) \times 180^\circ$ This formula calculates the total sum ($S$) of all interior angles in any convex polygon, where $n$ represents the number of sides of the polygon. We can divide a polygon into $n-2$ triangles by drawing diagonals from one vertex. Measure of One Interior Angle of a Regular Polygon $A = \frac{(n-2) \times 180^\circ}{n}$ This formula calculates the measure ($A$) of a single interior angle in a regular polygon. Since all interior angles in a regular polygon are equal, we divide the sum of all interior angles by the number of sides ($n$) (which is also the number of angles).