You can find the interior angle of a polygon when given its exterior angle by subtracting the exterior angle from 180 degrees.
At each vertex of a polygon, the interior angle and the corresponding exterior angle form a linear pair, meaning they lie on a straight line and their sum is always 180°. This relationship holds true for both regular and irregular polygons at any given vertex.
Based on the provided reference, the method is clearly stated:
Method for Finding Interior Angle from Exterior Angle
The most direct way to calculate an interior angle when the exterior angle is known is using their supplementary relationship.
- Interior Angle of a polygon = 180° – Exterior angle of a polygon.
This formula directly utilizes the fact that the interior and exterior angles at any single vertex add up to 180 degrees.
Example
Let's say you have a polygon, and at one particular vertex, the exterior angle measures 70°.
To find the interior angle at that same vertex:
- Start with the sum of the angles on a straight line: 180°.
- Subtract the given exterior angle.
- Interior Angle = 180° - 70° = 110°.
So, the interior angle at that vertex is 110°.
This method is universally applicable for finding the interior angle at a specific vertex of any polygon (regular or irregular) if you know the exterior angle at that same vertex.
While other methods exist for finding interior angles (such as using the number of sides 'n' for regular polygons: [180°(n) – 360°] / n, or by dividing the sum of interior angles by 'n'), the method involving the exterior angle is the most straightforward when the exterior angle value is provided.
