Question

Find x, find jl . any help is deeply appreciated :) !​

Answer 1

Answer:

6. x = 15

7. JL = 78

Step-by-step explanation:

6. 8x - 23 = ½(10x + 44) (midsegment theorem)

Multiply both sides by 2

2(8x - 23) = 10x + 44

16x - 46 = 10x + 44

Collect like terms

16x - 10x = 46 + 44

6x = 90

Divide both sides by 6

x = 90/6

x = 15

7. MN = 5x - 16

JL = 4x + 34

MN = ½(JL) (midsegment theorem)

5x - 16 = ½(4x + 34) (substitution)

2(5x - 16) = 4x + 34

10x - 32 = 4x + 34

Collect like terms

10x - 4x = 32 + 34

6x = 66

x = 66/6

x = 11

JL = 4x + 34

Plug in the value of x

JL = 4(11) + 34 = 44 + 34

JL = 78