This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify angle relationships to find x. Since line AB is parallel to line CD, the angle FMA and the angle MNE are corresponding angles. Therefore, they are equal. MNE = FMA = 5x Angles MNE and CNE form a linear pair on the straight line CD. Their sum is 180^. MNE + CNE = 180^ Step 2: Substitute the given values and solve for x. Substitute MNE = 5x and CNE = x+78^ into the equation from Step 1: 5x + (x+78^) = 180^ 6x + 78^ = 180^ Subtract 78^ from both sides: 6x = 180^ - 78^ 6x = 102^ Divide by 6: x = (102^)/(6) x = 17^ Step 3: Identify angle relationships to find y. Since line AB is parallel to line CD, the angle AMN and the angle DNM are alternate interior angles. Therefore, they are equal. AMN = DNM Angles CNE and DNM are vertically opposite angles. Therefore, they are equal. DNM = CNE = x+78^ From these relationships, we can write: AMN = x+78^ Step 4: Substitute the value of x and solve for y. We are given AMN = 4x+y. Equate this to the expression from Step 3: 4x+y = x+78^ Substitute the value of $