Question

find the number of sides of a regular polygon if the sum of its interior angle is 1)1260 2)1980 3)3420

Answer 1

Using the formula for the sum of interior angles of a polygon, we determine that a polygon with a 1260° angle sum has 9 sides, one with 1980° has 13 sides, and one with 3420° has 21 sides.

Step-by-step explanation:

To find the number of sides of a regular polygon given the sum of its interior angles, we use the formula: sum of interior angles = (n - 2) × 180°, where n is the number of sides of the polygon. This formula is derived from the fact that any polygon can be divided into triangles, each of which has an angle sum of 180°. Now, we solve for n in each case:

1. 1260° = (n - 2) × 180°
2. 1980° = (n - 2) × 180°
3. 3420° = (n - 2) × 180°

Solving each equation gives us the following number of sides:

1. For 1260°: n = 1260° / 180° + 2 = 7 + 2 = 9 sides
2. For 1980°: n = 1980° / 180° + 2 = 11 + 2 = 13 sides
3. For 3420°: n = 3420° / 180° + 2 = 19 + 2 = 21 sides