What is the point of E?

From the condition that $C$ is not in $\Gamma_2$ and $D$ is not in $\Gamma_1$ , we get that $E$ is on the opposite side of $CD$ as compared to $B$ . From the alternate segment theorem, $\angle DCE = \angle ACE = \angle ABC$ , and $\angle CDE = \angle ADE = \angle ABD$ . Thus $\begin{aligned} \angle CED &= 180^\circ - \angle CDE - \angle DCE \\ &= 180^\circ - \angle ABD-\angle ABC \\ &= 180^\circ - \angle CBD \\ &= 180^\circ - 71 ^\circ \\ &= 109 ^\circ \\ \end{aligned}$

Quadrilateral BCED will be formed from these tangent lines such that angle BCE and angle BDE are 90 degrees each (definition of tangent lines in a circle). Also, the sum of the measure of interior angles of a quadrilateral is 360, which includes angles BCE, BDE, CBD and CED. Since BCE = 90, BDE = 90, and CBD = 71, then m<CED = 360-90-90-71=109 degrees.