Question
Find the sum of the measure of the interior angles of each polygon. \( \begin{array}{l}\text { 7. Hexagon } \\ \text { 8. Decagon }\end{array} \)
Ask by Montgomery Joseph. in the United States
Feb 27,2025
Upstudy AI Solution
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Answer
The sum of the interior angles of a hexagon is 720°, and for a decagon, it's 1440°.
Solution
The formula to find the sum of the interior angles of any n-sided polygon is (n - 2) × 180°.
For a hexagon (6 sides):
Sum = (6 - 2) × 180° = 4 × 180° = 720°
For a decagon (10 sides):
Sum = (10 - 2) × 180° = 8 × 180° = 1440°
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Simplify this solution Bonus Knowledge
To find the sum of the measure of the interior angles of a polygon, you can use the formula: \( S = (n - 2) \times 180^\circ \), where \( S \) is the sum of the interior angles and \( n \) is the number of sides of the polygon. For a hexagon, \( n = 6 \): \[ S = (6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ \] For a decagon, \( n = 10 \): \[ S = (10 - 2) \times 180^\circ = 8 \times 180^\circ = 1440^\circ \] So the sum of the interior angles is 720° for a hexagon and 1440° for a decagon.
