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

In a regular polygon, all the interior angles have the same measure. Let n be the number of sides of the polygon, then we have: sum of all interior angles = (n - 2) x 180 degrees Each interior angle of the polygon is given as 140 degrees. Since the polygon is regular, it follows that all its interior angles are congruent. Hence, we can set up an equation involving the interior angle and solve for the number of sides n. In a regular polygon with n sides, the sum of the interior angles is given by: sum of all interior angles = n x (interior angle) Substituting the given value of the interior angle, we have: sum of all interior angles = n x 140 degrees We can now equate the two expressions for the sum of all interior angles: (n - 2) x 180 degrees = n x 140 degrees Expanding and simplifying the left side, we get: 180n - 360 = 140n Adding 360 to both sides and simplifying, we have: 40n = 360 Therefore, n = 9. Hence, the given polygon has 9 sides. Now, substituting this value of n in the expression for the sum of all interior angles, we have: sum of all interior angles = 9 x 140 degrees = 1260 degrees Therefore, the sum of all the interior angles of the given polygon is 1260 degrees. In conclusion, the answer is option (B) 1260 degrees.