If ΔABC ≅ ΔPQR, such that ∠ABC = 77°, ∠BCA = (x − y)°, AC = 48 cm, ∠PQR = (3x − 4)°, PR = x + 3y, then find the value of ∠QRP.​

Correct option is D

Given:

△ABC ≅ △PQR

∠ABC = 77^∘

∠BCA = (x − y)^∘

AC = 48 cm

∠PQR = (3x − 4)^∘

PR = x + 3y

Concept Used:

In congruent triangles, corresponding angles are equal and corresponding sides are equal.

Solution: 

Corresponding angles: ∠ABC = ∠PQR,  ∠BCA = ∠QRP

Corresponding sides: AC = PR

From angle correspondence:

∠ABC = ∠PQR

77^∘ = 3x − 4

3x = 81

x = 27

From side correspondence:

AC = PR

48 = x + 3y

3y = 21

y = 7

Now, using the corresponding angles:

∠BCA = ∠QRP

∠QRP = x − y = 27 − 7 = 20^∘