10 grade maths
Define the interior angle theorem.
Define the interior angle theorem.
1 Answer
Askiitians Tutor Team
The **Interior Angle Theorem** states that the sum of the interior angles of a polygon with \( n \) sides is given by the formula:
**Sum of Interior Angles = \( (n - 2) \times 180^\circ \)**
### Explanation:
1. A polygon can be divided into \( (n - 2) \) triangles by drawing diagonals from one vertex to all other non-adjacent vertices.
2. Since the sum of the angles of a triangle is \( 180^\circ \), the sum of all the interior angles of the polygon is the sum of the angles in these \( (n - 2) \) triangles.
### Example:
For a hexagon (\( n = 6 \)):
- Using the formula: Sum of interior angles = \( (6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ \).
Thus, the sum of the interior angles of a hexagon is \( 720^\circ \).
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