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Now that we've conquered exterior angles, let's quickly touch upon **interior angles** and how they relate to what we've learned. The interior angle is the angle inside the polygon. For each exterior angle, there is a corresponding interior angle. These two angles form a linear pair, which means they always add up to 180 degrees (because a straight line is 180 degrees). So, if you know the exterior angle, you can easily find the interior angle by subtracting the exterior angle from 180. For example, in our pentagon with a 72-degree exterior angle, the interior angle is 180 - 72 = 108 degrees. This relationship provides another way to approach polygon problems. By knowing the interior angle, you can also determine the number of sides, though the formula is slightly different. The sum of the interior angles of a polygon can be found using the formula: (n-2) * 180, where *n* is the number of sides. So for a pentagon, (5-2) * 180 = 540 degrees. Then to find each interior angle, you simply divide that sum by the number of sides. The relationships between exterior and interior angles offer a deeper understanding of polygons and the geometric principles at play. Understanding these connections enhances your problem-solving capabilities, allowing you to approach geometric problems from multiple angles (pun intended!). The fact that interior and exterior angles are connected by a simple relationship (adding up to 180 degrees) is another example of the internal consistency and beauty of geometry. With this understanding, you gain a fuller perspective of geometric shapes. The interplay between interior and exterior angles offers another layer of geometric exploration. Being able to go between interior and exterior angles enhances your ability to work with these shapes. It provides additional tools for problem-solving. This knowledge is useful, making your understanding of polygons more comprehensive.
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