Question

Figure JKLM is a parallelogram. The measures of line segments MT and TK are shown. What is the value of y?

Answer 1

Because JKLM is a parallelogram, MT = TK.

MT: 8y + 18
TK : 12y - 10

MT = TK
8y + 18 = 12y - 10
8y - 12y = -10 -18
-4y = -28
y = -28/-4
y = 7

MT: 8y + 18 → 8(7) + 18 = 56 + 18 = 74
TK : 12y - 10 → 12(7) -10 = 84 - 10 = 74

The value of y is 7.

Answer 2

We need to solve for the value of y in the given parallelogram where the measurements of segments MT and TK are given. We observed in the given figure, the two opposite parallel sides are equal in length such as length JK = length LM and length LK = length MJ.
Based on this evaluation, we can also say that the two diagonals are equal in length. Thus, we can write an expression:
segment MK = segment JL
replacing it with the given expression, we have:
8y + 18 = 12y -10
Transpose -10 to the left side and transpose 8y to the right side such as:
18 + 10 = 12y -8y
28 = 4y
divide both sides by 4, we have:
28 / 4 = 4y /4
7 = y

The value of y is 7".