Interior and exterior angles of polygons worksheet with answers – Embark on a mathematical journey with our comprehensive worksheet on interior and exterior angles of polygons. Delve into the captivating world of geometry as we explore the intricate relationship between these angles, equipping you with a profound understanding of polygonal shapes.
This meticulously crafted worksheet provides a thorough exploration of interior and exterior angles, their properties, and their applications in various fields. Prepare to unravel the secrets of polygons, one angle at a time.
Interior Angles of Polygons: Interior And Exterior Angles Of Polygons Worksheet With Answers
Interior angles are the angles formed by the intersection of two sides of a polygon. The sum of the interior angles of a polygon with nsides can be calculated using the formula 180°( n– 2).
Examples:
- Triangle (3 sides): 180°(3 – 2) = 180°
- Square (4 sides): 180°(4 – 2) = 360°
- Pentagon (5 sides): 180°(5 – 2) = 540°
Exterior Angles of Polygons
Exterior angles are the angles formed by the intersection of one side of a polygon and the extension of an adjacent side. The sum of the exterior angles of any polygon is always 360°.
Examples:
- Triangle: 3 exterior angles of 120° each, totaling 360°
- Square: 4 exterior angles of 90° each, totaling 360°
- Pentagon: 5 exterior angles of 72° each, totaling 360°
Relationship between Interior and Exterior Angles
The sum of the interior angles of a polygon is always 180° more than the sum of its exterior angles.
Formula:
Sum of interior angles = 180°( n– 2)
Sum of exterior angles = 360°
Therefore, sum of interior angles = sum of exterior angles + 180°
Applications of Interior and Exterior Angles
Understanding interior and exterior angles of polygons has various real-world applications:
- Architecture:Determining the shape and size of buildings and structures.
- Engineering:Designing bridges, tunnels, and other structures.
- Design:Creating logos, patterns, and other visual elements.
- Geometry and Trigonometry:Solving problems related to shapes, angles, and distances.
FAQ Guide
What is the relationship between interior and exterior angles of a polygon?
The sum of the interior angles of an n-sided polygon is (n-2) x 180 degrees, while the sum of the exterior angles is always 360 degrees.
How do I calculate the sum of interior angles of a polygon?
Use the formula: Sum of interior angles = (n-2) x 180 degrees, where n is the number of sides of the polygon.
What are some real-world applications of understanding interior and exterior angles of polygons?
Architects use these concepts to design buildings, engineers to construct bridges, and designers to create patterns and logos.
