Question

I need the steps to this, please. It says solve for x. Each figure is a parallelogram. Show your work.

Answer 1

With any parallelogram, the diagonals bisect each other. This is another way of saying that they cut each other in half.

FH is one diagonal that is split into two equal pieces by the other diagonal EG.

The two parts of FH (KH and KF) are congruent to each other, so KH = KF. They combine back to FH


By the segment addition postulate
KH + KF = FH
KH + KH = FH .... KF has been replaced with KH (works because KF = KH)
2*KH = FH

Now use substitution
2*KH = FH
2*15 = FH .... replace KH with 15 (since KH = 15)
2*15 = 4x-2 ... replace FH with 4x-2 (since FH = 4x-2)

and solve for x
2*15 = 4x-2
30 = 4x-2
30+2 = 4x-2+2 ... add 2 to both sides
32 = 4x
4x = 32
4x/4 = 32/4 ... divide both sides by 4
x = 8

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Answer: x = 8