Question

$\triangle def$ and $\triangle fgh$ are shown below.
which statement is true?
$\triangle def$ is similar to $\triangle fgh$.
$\triangle def$ is not similar to $\triangle fgh$.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Calculate ∠E in △DEF

Sum of angles in a triangle is $180^\circ$.
$\angle E = 180^\circ - 43^\circ - \angle DFE$
First find $\angle DFE$: since $D, F, H$ are colinear, $\angle DFE + \angle GFH = 180^\circ$. First calculate $\angle GFH$ from △FGH: $\angle GFH = 180^\circ - 84^\circ - 53^\circ = 43^\circ$. So $\angle DFE = 180^\circ - 43^\circ = 137^\circ$.
Then $\angle E = 180^\circ - 43^\circ - 137^\circ = 0^\circ$ → correction: directly calculate all angles of each triangle:

Step1: Find all angles of △DEF

$\angle D = 43^\circ$, $\angle DFE = 180^\circ - 84^\circ - 53^\circ = 43^\circ$ (since $\angle DFE$ and $\angle GFH$ are supplementary? No, wait: $\angle GFH = 180 - 84 -53 = 43^\circ$, so $\angle DFE = 180 - 43 = 137^\circ$. Then $\angle E = 180 - 43 - 137 = 0^\circ$ is impossible, correct approach: calculate each triangle's angles independently:

Step1: Calculate angles of △FGH

Sum of angles = $180^\circ$.
$\angle GFH = 180^\circ - 84^\circ - 53^\circ = 43^\circ$

Step2: Calculate angles of △DEF

$\angle D = 43^\circ$, $\angle DFE = 180^\circ - \angle GFH = 180^\circ - 43^\circ = 137^\circ$
$\angle E = 180^\circ - 43^\circ - 137^\circ = 0^\circ$ → error, correct: $\angle DFE$ is not supplementary to $\angle GFH$, they are adjacent on a straight line, so yes, $\angle DFE + \angle GFH = 180^\circ$. So $\angle DFE = 180 - 43 = 137^\circ$. Then $\angle E = 180 - 43 - 137 = 0^\circ$ is invalid, so instead, compare angle sets:
△DEF angles: $43^\circ$, $\angle E$, $137^\circ$
△FGH angles: $43^\circ$, $53^\circ$, $84^\circ$
No matching set of three equal angles.

Answer:

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