Short Answer 
To calculate the sum of the interior angles of an irregular polygon, use the formula x = (n Р2) √o 180¬∞, where n is the number of sides. For example, an irregular pentagon with 5 sides has a total interior angle sum of 540 degrees, and in a regular pentagon, each interior angle measures 108 degrees after dividing the total by the number of sides.
Step 1: Understand the Formula for Irregular Polygons
To calculate the sum of the interior angles of a polygon, particularly an irregular one, use the formula: x = (n Р2) √o 180¬∞. In this formula, n represents the number of sides in the polygon. This means that for an irregular polygon, the total measure of all interior angles can be derived by subtracting 2 from the number of its sides and then multiplying the result by 180 degrees.
Step 2: Calculate the Sum for a Specific Polygon
For example, to find the sum of the interior angles of an irregular pentagon (which has 5 sides), you can apply the formula discussed. The steps would be:
- x = (5 Р2) √o 180¬∞
- x = 3 √o 180¬∞
- x = 540°
This shows that the total sum of the interior angles in an irregular pentagon is 540 degrees.
Step 3: Use the Formula for Regular Polygons
If the pentagon is regular, you can still apply the same formula to find the sum of interior angles and then find the measure of each angle. For a regular pentagon, after calculating the total interior angles (540°), divide it by the number of sides:
- y = 540° ÷ 5
- y = 108°
This indicates that each interior angle of a regular pentagon measures 108 degrees, showcasing how to handle both regular and irregular polygons effectively.