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 — A. In ∆PQR ≅ ∆MON the letters pair off in written order: P↔M, Q↔O, R↔N. Match by position, not by resemblance.

∠PQR is the angle at Q, so its partner is the angle at O, written ∠MON:
5y − 8 = 82 → 5y = 90 → y = 18

QR joins the 2nd and 3rd letters, so it maps to ON:
3x + y = 24 → 3x + 18 = 24 → x = 2

x + y = 2 + 18 = 20 → option (a)

The 47° and 51° are never used; they only confirm 82 + 47 + 51 = 180.

Why the others are wrong

• (b)
  14 — 14 with 3x + y = 24 forces x = 5 and y = 9. But y is pinned by 5y − 8 = 82 at 18, so y = 9 is impossible.
• (c)
  18 — 18 is y on its own. The angle equation was matched correctly and the working stopped one line early — x = 2 still has to be added.
• (d)
  16 — 16 with 3x + y = 24 means x = 4 and y = 12, which would make ∠MON = 5(12) − 8 = 52° — not one of this triangle's angles (82°, 47°, 51°).

A congruence statement is read letter by letter. In ∆PQR ≅ ∆MON the first letters correspond, the second letters correspond, and the third letters correspond.

That single rule gives every pairing. An angle named by three letters sits at the middle letter, so ∠PQR (at Q) matches ∠MON (at O). A side named by two letters matches the side in the same two positions, so QR matches ON.

By CPCT — corresponding parts of congruent triangles — each matched pair is equal, which converts the geometry into two small linear equations.

Key facts

• In ∆PQR ≅ ∆MON the k-th letter of one name corresponds to the k-th letter of the other.
• ∠PQR is the angle at Q, so its congruent partner is ∠MON at O.
• Side QR corresponds to side ON, so ON = QR = 24.
• The stated angles are consistent: 82° + 47° + 51° = 180°.

Common traps

• Reading ∠MON as the angle at M because M is written first
• Pairing QR with MO or MN instead of ON
• Solving y = 18 and answering that, forgetting the question asks x + y

No directly related past PYQ was found.