Finding the Thevenin equivalent circuit for the following one
This statement and what follows is false:


  Then the current through the \$30\Omega\$ resistor is \$.567 \times 100/130 = .436\$ A


It looks like you are attempting to use a current divider (which is a correct approach) but you are using the wrong resistance. You need to use the equivalent resistance looking into the \$30\Omega\$ resistor, not just the \$30\Omega\$ resistor itself. That equivalent resistance is \$30\Omega + 40\Omega = 70\Omega\$ so the correct current divider is $$0.567\text{A} \times \frac{100\Omega}{100\Omega + 70\Omega} = 0.333\text{A}$$

You should be able to repeat this process to find the current through the leftmost \$20\Omega\$ resistor and then arrive at \$V_{\text{TH}}\$. Doing so I arrived at \$V_{\text{TH}} = 10\$V.