Answer:

n ≈ 2

Approximately 2.

Step-by-step explanation:

To find the number of sides of a polygon given the sum of the measures of the interior angles, we can use the formula:

Sum of interior angles = (n - 2) * 180 degrees,

where n is the number of sides of the polygon.

Let's plug in the given values and solve for n:

1.540° + 6.1800° + 2.1260° + 7.3240° + 3.1980° + 8.720° + 4.2520° + 9.1440° + 5.1080° + 10.2160° = (n - 2) * 180 degrees.

57.8580° = (n - 2) * 180 degrees.

2. Divide both sides of the equation by 180:

57.8580° / 180 = n - 2.

57.8580° / 180 = n - 2.0.32143 = n - 2.

Add 2 to both sides of the equation:

0.32143 + 2 = n.

0.32143 + 2 = n.n = 2.32143.

Since the number of sides of a polygon must be a whole number, we round the value of n to the nearest whole number:

n ≈ 2

Therefore, the number of sides of the polygon is approximately 2.

Correct me if I'm Incorrect.