Exterior angles

Exterior Angles

• Exterior angles are the angles formed outside a shape, usually a polygon, when a side is extended.
• The term is often related to polygons, notably triangles, where it is easier to visualise.
• There is always one exterior angle at each vertex of a polygon.

Sum of Exterior Angles

• A key property is that the sum of the exterior angles of any polygon is always equal to 360 degrees.
• This makes sense when considering a polygon such as a hexagon where one can imagine a point slowly rotating around, landing on each vertex in turn, and making a full 360 degree turn.

Triangle Exterior Angles

• In a triangle, the exterior angle at each vertex is equivalent to the sum of the two interior opposite angles.
• For instance, if a triangle has interior angles of 40, 70 and 70 degrees, the exterior angle at the vertex with the 70 degree angle is the sum of the other two angles, i.e., 40 + 70 = 110 degrees.

Practical Applications

• Understanding exterior angles is useful for various real-life applications, such as architecture, engineering, and computer graphics.
• Recognising and calculating these angles precisely can help to create and validate complex designs and structures.

Revise the core concepts related to exterior angles and continually practice problems associated with them to reinforce these concepts. Always keep in mind the fundamental rule of exterior angles, especially for polygons.