MATHAthe The sum of intorior anyles of polygon is 1980 Find the number of triangle the polyyon can be subdivided into

To find the number of triangles a polygon can be subdivided into, we can use the formula for the sum of the interior angles of a polygon, which is given by: \[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \] where \( n \) is the number of sides of the polygon. Given that the sum of the interior angles is 1980 degrees, we can set up the equation: \[ (n - 2) \times 180 = 1980 \] Now, we can solve for \( n \): 1. Divide both sides by 180: \[ n - 2 = \frac{1980}{180} \] 2. Calculate the right side: \[ n - 2 = 11 \] 3. Add 2 to both sides: \[ n = 13 \] So, the polygon has 13 sides. To find the number of triangles the polygon can be subdivided into, we can use the fact that any polygon can be divided into \( n - 2 \) triangles. Therefore, for a polygon with 13 sides: \[ \text{Number of triangles} = n - 2 = 13 - 2 = 11 \] Thus, the polygon can be subdivided into **11 triangles**.