1.3a Exterior and Interior Angles of Polygons
LEARNING OBJECTIVES
- Identify exterior angles and its adjacent interior angles of a polygon.
- Explain the relationship between exterior angles and its adjacent interior angles.
Interior Angles of a Polygon
Interior angles are the angles located inside the polygon, formed by two adjacent sides.
Exterior Angles of a Polygon
When we talk about exterior angles, we are referring to angles formed when one side of the polygon is extended outward. Imagine drawing a line from one vertex of a polygon and extending it outside the shape. The angle formed between this extended line and the adjacent side is called the exterior angle.
The sum of the exterior angle and its adjacent interior angle in any polygon is always 180°.
Drag any vertex and observe what happens to the sum of the exterior angle and its adjacent interior angle.
The sum of all exterior angles in any polygon, regardless of the number of sides, is always 360°.
This means that if you measure the exterior angles of any polygon and add them together, they will equal 360°! Interact with the different polygons below to verify if the sum of all exterior angles is indeed 360°. Note that one full revolution around a circle is equal to 360°.
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