a.
Let's call the intersection point of the chords M.
In order to calculate the arc AB, we can use the following property:
[tex]\angle AMB=\frac{AB+CD}{2}[/tex]Since ∠AMB is 86° and CD = 30°, we have:
[tex]\begin{gathered} 86=\frac{AB+30}{2} \\ AB+30=172 \\ AB=172-30 \\ AB=142\degree \end{gathered}[/tex]b.
In order to find DC, let's use the same formula, with ∠AMB = 86° and AB = 135°:
[tex]\begin{gathered} 86=\frac{135+DC}{2} \\ 135+DC=172 \\ DC=172-135 \\ DC=37\degree \end{gathered}[/tex]