Question

determine if triangle $bcd$ and triangle $efg$ are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)
answer attemp
are
are not
the triangles $\boldsymbol{vee}$ similar.

Explanation:

Step1: Find ∠B in △BCD

Sum of angles in a triangle is $180^\circ$.
$\angle B = 180^\circ - 58^\circ - 69^\circ = 53^\circ$

Step2: Find ∠G in △EFG

Sum of angles in a triangle is $180^\circ$.
$\angle G = 180^\circ - 53^\circ - 69^\circ = 58^\circ$

Step3: Compare triangle angles

In △BCD: $\angle B=53^\circ$, $\angle C=69^\circ$, $\angle D=58^\circ$
In △EFG: $\angle E=53^\circ$, $\angle F=69^\circ$, $\angle G=58^\circ$
All corresponding angles are equal.

Answer:

The triangles are similar, by the AA (Angle-Angle) similarity criterion (all corresponding angles are congruent).