In an isosceles trapezoid, the base angles have the same measure pairwise.
The sum of the interior angles of a quadrilateral is 360º
For the given trapezoid:
[tex]\begin{gathered} m\angle A+m\angle B+m\angle C+m\angle D=360 \\ \\ m\angle A=m\angle D \\ m\angle B=m\angle C \end{gathered}[/tex]
Given angle B has a measure of 110º
[tex]m\angle B=m\angle C=110[/tex][tex]\begin{gathered} 2m\angle A+2m\angle B=360 \\ \\ 2m\angle A+2(110)=360 \end{gathered}[/tex]
Use the equation above to find the measure of angle A:
[tex]\begin{gathered} 2m\angle A+220=360 \\ 2m\angle A=360-220 \\ 2m\angle A=140 \\ m\angle A=\frac{140}{2} \\ \\ m\angle A=70 \\ \\ m\angle A=m\angle D=70 \end{gathered}[/tex]
Then, the measures of missing angles are:
[tex]\begin{gathered} m\angle A=70 \\ m\angle C=110 \\ m\angle D=70 \end{gathered}[/tex]
