Reviewed by Jo-ann Caballes
What is the sum of the interior angles of a hexagon?
Answer: The sum of the interior angles of a hexagon is 720 degrees
A hexagon is a polygon with six sides. The sum of its interior angles can be calculated using geometry formulas for polygons. Understanding the sum of the interior angles is essential for solving many geometric problems involving hexagons and other polygons.
Methods
Math Tutor Explanation Using the Polygon Angle Sum Formula
The sum of the interior angles of any polygon can be determined using a general formula that relates to the number of sides.
Step 1: Step 1: Count the number of sides in the hexagon (n = 6)
Step 2: Step 2: Use the formula: (n - 2) × 180 degrees
Math Tutor Explanation Using Triangulation
A polygon can be divided into triangles, each of which has an angle sum of 180 degrees. The total sum is based on how many such triangles can be formed inside the hexagon.
Step 1: Step 1: Draw all possible diagonals from a single vertex in the hexagon to divide it into triangles
Step 2: Step 2: Notice that a hexagon can be split into 4 triangles
Step 1:
Step 2:
Math Tutor suggests: Explore Interior Angles of Polygons
Strengthen your understanding of polygon angle sums with these related questions and exercises.
FAQ on Interior Angles of Polygons
What is the formula for the sum of the interior angles of a polygon?
The formula is (n - 2) × 180 degrees, where n is the number of sides.
How many degrees is each interior angle in a regular hexagon?
In a regular hexagon, each interior angle is 120 degrees.
Can the sum of the interior angles be negative?
No, the sum of the interior angles of any polygon is always a positive number.
Why does a hexagon have 4 triangles when divided from one vertex?
Because you can draw diagonals to 3 non-adjacent vertices, dividing the hexagon into 4 triangles.
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