Question

If the sum of the interior angles of a regular polygon measures up to 1440 degrees, how many sides does the polygon have?

Answer 1

Answer:

Option 1) 10 sides

Step-by-step explanation:

We are given a regular polygon. The sum of interior angles measure upto 1440 degrees.

Since it is a regular polygon, it satisfies the following properties:

• All the sides are equal.
• All interior angle have same measure.

Let the regular polygon have n sides.

Then, the sum of interior angle is given by:

$(n-2)\times 180^\circ$

Putting the values, we get,

$(n-2)\times 180 = 1440\\\\n-2 = \dfrac{1440}{180}\\\\n-2 = 8\\n = 8 + 2\\n =10$

Thus, there are 10 sides. The regular polygon is a regular decagon.