If ∆PQR≅∆MON such that ∠PQR = 82°, ∠QRP = 47°, ∠RPQ = 51°, ∠MON = (5y - 8)°, QR = 24 and ON = 3x + y, then find (x + y).

Correct option is D

Given:

​∆PQR≅∆MON

∠PQR = 82°, ∠QRP = 47°, ∠RPQ = 51°, ∠MON = (5y - 8)°, QR = 24 and ON = 3x + y

Solution:

As both the triangles are congruent, so their sides and angles will be equal to the corresponding angles/sides.

So, in these triangles,

∠MON = ∠PQR

5y - 8 = 82

5y = 82 + 8 = 90

y = $$\frac{90}{5}=18^\degree$$

Similarly,

QR = ON

Now, 3x + y = 24

3x + 18 = 24

3x = 24 - 18 = 6

x = $$\frac{6}{3}=2$$​​

So, x + y = 18 + 2 = 20