Interior angles of polygons

Learning Objectives Identify and classify different types of polygons based on their number of sides. Define an interior angle of a polygon and locate it within various shapes. Discover the relationship between the number of sides of a polygon and the sum of its interior angles. Apply the formula $(n-2) \times 180^\circ$ to calculate the sum of interior angles for any polygon. Calculate the measure of a single interior angle in a regular polygon. Solve for unknown interior angles in irregular polygons using algebraic reasoning. Have you ever wondered why a soccer ball is made of pentagons and hexagons, or why floor tiles fit together perfectly? ⚽️ It all comes down to the angles inside these shapes! In this lesson, you'll learn about the 'interior angles' of...

TermDefinitionExample PolygonA closed two-dimensional figure made up of three or more straight line segments.A triangle, square, pentagon, and octagon are all examples of polygons. SideA straight line segment that forms part of the boundary of a polygon.A square has 4 sides, and a hexagon has 6 sides. VertexA point where two sides of a polygon meet.A triangle has 3 vertices (corners), and a quadrilateral has 4 vertices. Interior AngleAn angle formed inside a polygon by two adjacent sides meeting at a vertex.In a square, each interior angle measures $90^\circ$. Regular PolygonA polygon where all sides are equal in length and all interior angles are equal in measure.An equilateral triangle (3 equal sides, 3 equal angles) or a square (4 equal sides, 4 equal angles). Irregular PolygonA polygo...

Sum of Interior Angles of a Triangle $S = 180^\circ$ The sum of the measures of the three interior angles of any triangle is always $180^\circ$. This is the fundamental building block for understanding other polygons. Sum of Interior Angles of an n-sided Polygon $S = (n-2) \times 180^\circ$ To find the total sum of all interior angles in any polygon, subtract 2 from the number of sides ($n$), then multiply the result by $180^\circ$. This formula works for any polygon with $n \ge 3$ sides. Measure of One Interior Angle of a Regular n-sided Polygon $A = \frac{(n-2) \times 180^\circ}{n}$ For a regular polygon (where all angles are equal), first find the sum of all interior angles using $(n-2) \times 180^\circ$, then divide that sum by the number of sides ($n$) to find t...