Answer:
AD = 230
Explanation:
AD = 30x - 10
MN = 31x + 1
BC = 30x + 28
To find the length of AD, we need to generate an equation that will enable us to find the value of x.
Thus,
MN = ½(AD + BC) => Trapezoid Midsegment Theorem
Plug in the values
31x + 1 = ½(30x - 10 + 30x + 28)
(31x + 1) × 2 = 30x - 10 + 30x + 28
62x + 2 = 30x - 10 + 30x + 28
Add like terms
62x + 2 = 60x + 18
62x - 60x = -2 + 18
2x = 16
x = 16/2
x = 8
✅AD = 30x - 10
Plug in the value of x
AD = 30(8) - 10 = 230