Question

in $\triangle cde, \overline{ec} \cong \overline{de}$ and $m\angle d = 34^\circ$. find $m\angle c$.

Explanation:

Step1: Identify triangle type

$\triangle CDE$ is isosceles (since $\overline{EC} \cong \overline{DE}$)

Step2: Match congruent sides to angles

Sides $\overline{EC} \cong \overline{DE}$ correspond to $\angle D$ and $\angle C$ respectively. In isosceles triangles, angles opposite congruent sides are congruent.

Answer:

$\mathrm{m}\angle C = 34^\circ$