In geometry, an exterior angle of a polygon is formed when one side of the polygon is extended. The exterior angle is the angle formed between this extended side and the adjacent side of the polygon.
For any polygon, the sum of the exterior angles is always 360 degrees, regardless of the number of sides. When dealing with a triangle, the exterior angle is equal to the sum of the two opposite (non-adjacent) interior angles.
Here's a quick overview of how to find and work with exterior angles:
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Finding an Exterior Angle: If you know one of the interior angles, you can find the exterior angle by subtracting the interior angle from 180 degrees (since interior and exterior angles are supplementary). \[ \text{Exterior Angle} = 180^\circ - \text{Interior Angle} \]
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Sum of Exterior Angles: For any polygon, the formula for the sum of the exterior angles (one at each vertex) is: \[ \text{Sum of Exterior Angles} = 360^\circ \]
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Usage in Triangles: For a triangle, if the interior angles are \( A \), \( B \), and \( C \), then the exterior angle \( D \) at one vertex is given by: \[ D = 180^\circ - A \] Here, the exterior angle \( D \) can also be expressed in terms of the other two interior angles: \[ D = B + C \]
If you have specific scenarios or examples related to exterior angles that you would like to discuss, feel free to ask!