To determine the similarity between the two triangles, we first need to calculate the missing angles.
In triangle \(ABC\):
- Given \(m\angle A = 47^\circ\) and \(m\angle B = 36^\circ\).
- We can find \(m\angle C\) using the triangle sum theorem (the sum of the angles in a triangle is \(180^\circ\)):
\[ m\angle C = 180^\circ - m\angle A - m\angle B = 180^\circ - 47^\circ - 36^\circ = 97^\circ \]
Now we have the angles for triangle \(ABC\):
- \(m\angle A = 47^\circ\)
- \(m\angle B = 36^\circ\)
- \(m\angle C = 97^\circ\)
In triangle \(GHJ\):
- Given \(m\angle G = 36^\circ\) and \(m\angle J = 97^\circ\).
- We can find \(m\angle H\) using the same theorem:
\[ m\angle H = 180^\circ - m\angle G - m\angle J = 180^\circ - 36^\circ - 97^\circ = 47^\circ \]
Now we have the angles for triangle \(GHJ\):
- \(m\angle G = 36^\circ\)
- \(m\angle H = 47^\circ\)
- \(m\angle J = 97^\circ\)
Now we can compare:
- \(m\angle A = 47^\circ \leftrightarrow m\angle H = 47^\circ\)
- \(m\angle B = 36^\circ \leftrightarrow m\angle G = 36^\circ\)
- \(m\angle C = 97^\circ \leftrightarrow m\angle J = 97^\circ\)
Since all corresponding angles of triangle \(ABC\) and triangle \(GHJ\) are equal, we have:
\[ \triangle ABC \sim \triangle GHJ \]
Thus, the correct response is:
\[ \triangle ABC \sim \triangle GHJ \]