Each of the interior angles of a regular polygon is 140o. Calculate the sum of all the interior angles of the polygon

Answer Details

In a regular polygon, all interior angles are congruent (i.e., have the same measure). Let's call the measure of one interior angle of the polygon "x". Since the polygon is regular, we know that it has n sides, where n is a positive integer. We can use the formula for the sum of interior angles of a polygon, which is: Sum of interior angles = (n-2) * 180 degrees Since each interior angle in this polygon measures 140 degrees, we can set up an equation: x = 140 We can then solve for the number of sides by using the fact that the sum of the interior angles is also equal to: (n) * (x) = n * 140 And since the sum of the interior angles is also equal to: (n-2) * 180 We can set these two expressions equal to each other and solve for n: n * 140 = (n-2) * 180 140n = 180n - 360 40n = 360 n = 9 Therefore, the polygon has 9 sides, and the sum of the interior angles is: (n-2) * 180 = (9-2) * 180 = 1260 degrees So the correct answer is 1260 degrees.