If the interior angles of hexagon are 107°, 2x°, 150°, 95°, (2x-15)° and 123°, find x.

Answer Details

The sum of the interior angles of a hexagon is given by the formula (n-2) x 180, where n is the number of sides of the polygon. Therefore, for a hexagon (6 sides), the sum of the interior angles is (6-2) x 180 = 720 degrees. We are given five of the six interior angles of the hexagon: 107°, 2x°, 150°, 95°, and (2x-15)°. We can use these angles to set up an equation and solve for x: 107° + 2x° + 150° + 95° + (2x-15)° + sixth angle = 720° Simplifying, we get: 339° + 4x = 720° Subtracting 339 from both sides, we get: 4x = 381° Dividing both sides by 4, we get: x = 95.25° None of the answer choices match this exact value, but we can round it to the nearest degree to get 95°, which corresponds to choice (b). Therefore, the answer is: - \(65^{\circ}\)