a) 5x b) GH=9 and JK=15
Work Step by Step
We can find GK by adding GH and HK because of the Segment Addition Postulate. To find GH, we can do GJ-HJ to get x+3. HK is 4x-3. GH+HK=5x. $GK=5x$ If GK=30 and GK=5x, then $5x=30$ by substitution, and x=6. We established that GH=x+3. Substituting 6 into the equation gives GH=9. To find JK, we can do HK-HJ to get 3x-3. JK is 3x-3. Substituting 6 into the equation gives JK=15.