jmc

Angles $BAC$ and $BCA$ are each inscribed angles, so each one is equal to half of the measure of the arc they subtend. Therefore, the measures of arcs $AB$ and $BC$ are each 70 degrees, and together, the measure of arc $ABC$ is 140 degrees. Notice that angle $CDA$ is also an inscribed angle, and it subtends arc $ABC$, so $m\angle CDA=\frac{1}{2}(\text{arc }ABC)=(1/2)(140)=\boxed{70}$ degrees.