If ∆PQR ≅ ∆MON such that ∠PQR = 82°,∠QRP = 47°,∠RPQ = 51°,∠MON = (5y - 8)°,QR = 24 and ON = 3x + y, then find (x + y).
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 20.
Since the triangles are congruent (ΔPQR ≅ ΔMON), the corresponding angles are equal:
⇒ ∠PQR = ∠MON = 82°
⇒ ∠QRP = ∠ONM = 47°
⇒ ∠RPQ = ∠MNO = 51°
From the given question,
⇒ ∠MON = 5y - 8
⇒ 82° = 5y - 8
⇒ 5y = 90°
⇒ y = 18°
Since the triangles are congruent, the corresponding sides are also equal
⇒ QR = ON
⇒ QR = 24° and ON = 3x + y
⇒ 24° = 3x + y [y = 18]
⇒ 24° = 3x + 18
⇒ 3x = 6
⇒ x = 2
Thus, the value of x + y = 2 + 18 = 20