Question

△ceg and △def are shown below.
which statement is true?
△ceg is similar to △def.
△ceg is not similar to △def.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Find $\angle DFE$ in $\triangle DEF$

Sum of angles in a triangle is $180^\circ$.
$\angle DFE = 180^\circ - 64^\circ - 64^\circ = 52^\circ$

Step2: Find $\angle C$ in $\triangle CEG$

$\angle CEG = 64^\circ$, $\angle G = 54^\circ$.
$\angle C = 180^\circ - 64^\circ - 54^\circ = 62^\circ$

Step3: Compare triangle angle sets

$\triangle DEF$ angles: $64^\circ, 64^\circ, 52^\circ$
$\triangle CEG$ angles: $64^\circ, 54^\circ, 62^\circ$
No matching 3-angle pairs for similarity.

Answer:

$\triangle CEG$ is not similar to $\triangle DEF$.