This document provides an overview of polygons, defining them as closed shapes made of straight sides and explaining the relationship between the number of sides and angles. It includes information on measuring angles, calculating interior and exterior angles, and gives examples of regular polygons. Additionally, it highlights the presence of polygons in real life and offers review questions for learners.

1. Exploring Polygons: Angles and Sides

2. What is a Polygon?
● A polygon is a closed shape with straight
sides
● Made up of line segments that don't cross
each other
● Examples: triangles, squares, pentagons,
hexagons
● Can you think of any objects around you
that are shaped like polygons?

3. Sides of Polygons
● The number of sides determines the
polygon's name
● Triangle: 3 sides
● Quadrilateral: 4 sides
● Pentagon: 5 sides
● Hexagon: 6 sides
● Can you guess how many sides an
octagon has?

4. Angles in Polygons
● An angle is formed where two sides meet
● Each polygon has the same number of angles as sides
● Interior angles: angles inside the polygon
● Exterior angles: angles outside the polygon
● How many angles does a rectangle have?

5. Measuring Angles
● Angles are measured in degrees
● Use a protractor to measure angles
● A full circle has 360 degrees
● Right angle = 90 degrees
● Can you find any right angles in your
classroom?

6. Sum of Interior Angles
● The sum of interior angles depends on the number of sides
● Formula: (n - 2) × 180°, where n is the number of sides
Triangle: (3 - 2) × 180° = 180°
Square: (4 - 2) × 180° = 360°
● What's the sum of interior angles in a pentagon?

7. Regular Polygons
● All sides are equal in length
● All interior angles are equal
● Examples: equilateral triangle, square,
regular pentagon
● Can you draw a regular hexagon?

8. Calculating Interior Angles of Regular Polygons
● Formula: (n - 2) × 180° ÷ n, where n is the number of sides
● Square: (4 - 2) × 180° ÷ 4 = 90°
● Regular Pentagon: (5 - 2) × 180° ÷ 5 = 108°
● Try calculating the interior angle of a regular octagon!

9. Exterior Angles of
Polygons
● Exterior angle + Interior angle = 180°
● Sum of all exterior angles of any polygon
= 360°
● In regular polygons, all exterior angles are
equal
● Can you explain why the sum is always
360°?

10. Polygons in Real Life
● Road signs: octagon (stop sign), triangle
(yield sign)
● Sports: pentagon (soccer ball panels)
● Nature: hexagon (honeycomb cells)
● Architecture: various polygon shapes in
buildings
● Can you spot 3 polygons in this classroom
right now?

11. Review and Practice
● Name a polygon with 7 sides (heptagon)
● Calculate the sum of interior angles of a hexagon
● Measure angles of various polygons using a protractor
● Draw and label different types of polygons
● How many triangles can you see in a regular hexagon?