Step-by-step explanation:
Sum of currents entering a node = sum of currents leave the node
0.20 = I₁ + I₂
Sum of voltage gains and voltage drops around a loop = 0
Left loop:
6 − 100I₁ = 0
Outer loop:
6 − 3 − I₂R = 0
Solving the second equation:
I₁ = 0.06 A
Plug into the first equation:
I₂ = 0.14 A
Plug into the third equation:
R = 21.4 Ω