Answer :
[tex]m\angle L1\cong m\angle L4=85.8[/tex]
1) Since we have two parallel lines intercepted by a transversal one. Then we can state that:
m∠L3 +m∠L4 =180º as well as m∠L1 +m∠L2 =180º, are supplementary ones.
[tex]\begin{gathered} m\angle L3+m\angle L4=180º \\ 94.2+m\angle L4=180º \\ 94.2-94.2+m\angle L4=180-94.2 \\ m\angle L4=85.8 \end{gathered}[/tex]Similarly:
[tex]\begin{gathered} m\angle L1+m\angle L2=180º \\ 85.8+m\angle L2=180º \\ m\angle L2=180º-85.8 \\ m\angle L2=94.2 \end{gathered}[/tex]And therefore:
[tex]\begin{gathered} m\angle L2\cong m\angle L3 \\ m\angle L1\cong m\angle L4 \end{gathered}[/tex]2) Hence, we can state that m∠L2 ≅m∠L3 as well as m∠L1 ≅m∠L4. Since corresponding angles are congruent then we can conclude that m∠L1 ≅m∠L4 are corresponding angles.
3) Hence, the answer is
[tex]m\angle L1\cong m\angle L4=85.8[/tex]