We know that
[tex]\angle A\cong\angle C[/tex]So,
[tex]\angle A\cong\angle C\text{ }\rightarrow\text{ 8b=112 }\rightarrow\text{ b=112/8 }\rightarrow\text{ b=}14[/tex]Because we are working with a quadrilateral, we also know that
[tex]\angle A+\angle B+\angle C+\angle D=360[/tex]But we already know that
[tex]\angle A=\angle C=112[/tex]And since we have two equal angles in a quadrilateral, we have no other option but for the remaining 2 angles to be equal. That means that
[tex]AB=CD\text{ }\rightarrow\text{ 2a=34 }\rightarrow\text{ a=34/2 }\rightarrow\text{ a=17}[/tex]Hence,
[tex]a=17\text{ , b=14}[/tex]