In a polygon, if the sum of the interior angles is 720 degrees, how many sides does the polygon have? (2023)
Practice Questions
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In a polygon, if the sum of the interior angles is 720 degrees, how many sides does the polygon have? (2023)
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The formula for the sum of the interior angles of a polygon is (n-2) * 180, where n is the number of sides. Setting (n-2) * 180 = 720 gives n = 6.
Questions & Step-by-step Solutions
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Q: In a polygon, if the sum of the interior angles is 720 degrees, how many sides does the polygon have? (2023)
Solution: The formula for the sum of the interior angles of a polygon is (n-2) * 180, where n is the number of sides. Setting (n-2) * 180 = 720 gives n = 6.
Steps: 6
Step 1: Understand that the sum of the interior angles of a polygon can be calculated using the formula (n-2) * 180, where n is the number of sides.
Step 2: We know the sum of the interior angles is 720 degrees. So we can set up the equation: (n-2) * 180 = 720.
Step 3: To solve for n, first divide both sides of the equation by 180: (n-2) = 720 / 180.
Step 4: Calculate 720 divided by 180, which equals 4. So now we have: n - 2 = 4.
Step 5: To find n, add 2 to both sides of the equation: n = 4 + 2.
Step 6: Calculate 4 + 2, which equals 6. Therefore, the polygon has 6 sides.
