Find the value of x.(The figure may not be drawn to scale.) 4. a. 131 b. 62 c. 47 d. 60

To find the value of , we need to use the information given about the angles in the hexagon and the properties of triangles and polygons.Step 1: Calculate the angle at B in triangle ABC.Since the sum of angles in any triangle is 180°, we can find the angle at B by subtracting the other two angles from 180°.Angle CBA = 60°Angle BAC = 46°Angle ABC = 180° - Angle CBA - Angle BACAngle ABC = 180° - 60° - 46°Angle ABC = 74°Step 2: Calculate the sum of interior angles of the hexagon.The sum of interior angles of an n-sided polygon is given by the formula:\(S = (n - 2) \times 180°\)For a hexagon, , so:\(S = (6 - 2) \times 180°\) Step 3: Calculate the sum of the known angles in the hexagon.We know the following angles:Angle CBA = 60°Angle ABC = 74° (from Step 1)Angle BAC = 46°Angle EFD = 78°Sum of known angles = Angle CBA + Angle ABC + Angle BAC + Angle EFDSum of known angles = 60° + 74° + 46° + 78°Sum of known angles = 258°Step 4: Calculate the sum of the unknown angles in the hexagon.Since the sum of all angles in the hexagon is 720°, the sum of the unknown angles is:Sum of unknown angles = Sum of interior angles of hexagon - Sum of known anglesSum of unknown angles = 720° - 258°Sum of unknown angles = 462°Step 5: Express the unknown angles in terms of .The unknown angles are CED and DEF.Angle CED = °Angle DEF = °Step 6: Set up the equation and solve for .Sum of unknown angles = Angle CED + Angle DEF462° = + Combine like terms:462° = 2 - 13Add 13 to both sides:462° + 13 = 2 475° = 2 Divide both sides by 2: = 475° / 2 = 237.5°However, this value for does not make sense in the context of the problem, as it would imply that the angles in the hexagon exceed the sum of 720°. This suggests that there may be an error in the interpretation of the picture details or the question itself. Since none of the answer choices match this result, and given that the angles in a hexagon must sum to 720°, we need to re-evaluate the information provided.Please double-check the picture details and the question to ensure that all the information is accurate and complete. If there is additional information or if the details provided are incorrect, please provide the correct details so that we can solve the problem accurately.