The missing measures in the given triangles are,
BN = 9 cm
TW = 14 cm
BF = 12 cm
m ∠W = 82°
m ∠B = 67°
m ∠F = 31°
What is isomorphic triangles?
The triangulations of two simple polygons, Tp and Tq, are referred to as isomorphic (or occasionally compatible) if an isomorphism exists between the vertices of P and Q, and the isomorphism has the property that three vertices of P form a triangle in Tp if and only if the mapping of the three vertices in Q also form a triangle in Tq.
Given: ΔSTW ≅ ΔBFN
We have to find the missing measure.
As the triangles are isomorphic.
⇒ All sides and angles of two triangles are same.
⇒ ST ≅ BF, TW ≅ FN, SW ≅ BN
∠S ≅∠B, ∠T ≅ ∠F, ∠W ≅ ∠N
As SW = 9 cm ⇒ BN = 9 cm
As FN = 14 cm ⇒ TW = 14 cm
As ST = 12 cm ⇒ BF = 12 cm
As m ∠N = 82° ⇒ m ∠W = 82°
As m ∠S = 67° ⇒ m ∠B = 67°
Now m ∠F = 180° - 67° - 82°
⇒ m ∠F = 31°
Hence, the missing measures in the given triangles are,
BN = 9 cm
TW = 14 cm
BF = 12 cm
m ∠W = 82°
m ∠B = 67°
m ∠F = 31°
Complete question:
Complete question is attached below.