Each interior angle of a regular polygon is 162°. Find the sum of all the interior angles

Answer 1

Let's assume that the regular polygon has n sides.

The formula to find the sum of the interior angles of a polygon is given by:

Sum = (n-2) * 180°

Given that each interior angle of the regular polygon is 162°, we can set up the following equation:

162° = (n-2) * 180°

Simplifying the equation:

162° = 180°n - 360°

Rearranging the equation:

180°n = 162° + 360°
180°n = 522°

Dividing both sides by 180°:

n = 522° / 180°
n ≈ 2.9

Since the number of sides of a polygon must be a whole number, we round the value of n to the nearest whole number, which is 3.

Therefore, the regular polygon has 3 sides, which is an equilateral triangle.

Now, we can find the sum of the interior angles by using the formula:

Sum = (n-2) * 180°
Sum = (3-2) * 180°
Sum = 180°

So, the sum of all the interior angles of the regular polygon is 180°.