What is the sum of the interior angles of the polygon shown below?
Answer (1)
Answer:To find the sum of the interior angles of a polygon, you can use the formula:\text{Sum of interior angles} = (n - 2) \times 180^\circwhere n is the number of sides of the polygon.If you provide the number of sides or an image of the polygon, I can calculate the sum for you.Step-by-step explanation:Here's a step-by-step explanation of how to calculate the sum of the interior angles of a polygon:Step 1: Identify the number of sides (n) of the polygonThe first step is to determine how many sides the polygon has. The number of sides will be represented as n.Step 2: Apply the formula for the sum of interior anglesThe formula to calculate the sum of the interior angles of any polygon is:\text{Sum of interior angles} = (n - 2) \times 180^\circThis formula works because a polygon can be divided into triangles, and each triangle's interior angles add up to . For any polygon with sides, it can be divided into triangles.Step 3: Plug in the number of sides (n) into the formulaSubstitute the number of sides n of the polygon into the formula. For example, if you have a hexagon (which has 6 sides), the calculation would look like this:\text{Sum of interior angles} = (6 - 2) \times 180^\circ\text{Sum of interior angles} = 4 \times 180^\circ = 720^\circ ]Step 4: Interpret the resultThe result of the calculation gives you the total sum of the interior angles for that specific polygon. For a hexagon, the sum of the interior angles is .Example for a different polygon:If the polygon has 8 sides (an octagon), the steps are:1. Identify .2. Use the formula:\text{Sum of interior angles} = (8 - 2) \times 180^\circ = 6 \times 180^\circ = 1080^\circThus, the sum of the interior angles of an octagon is .By following these steps, you can calculate the sum of interior angles for any polygon.
