Solve for x in the following trapezoid. Assume QP is a mid segment.

X = 2

Using the trapezoid mid segment theorem, knowing that the mid segment is parallel to the bases and half as long as the sum of the lengths of the bases, we add the lengths of the two bases and set it equal to two times the length of the mid segment.

7x+3+ 15= 16(2)

7x+18= 32

Subtract 18 from both sides.

7x = 14

Divide both sides by 7.

X = 2.

You can check your work by solving for the length of the base 7x + 3.

7(2)+3 =17

Then, add the length of the two bases together.

15 + 17 = 32. Half of 32 equals sixteen, which is your mid segment.

(correct me if i’m wrong, i got the theorem off of the internet and did the rest of the work myself.)