△ABC and △PQR are respectively congruent. If AB = 8 = PQ, BC = 10 = QR and ∠B = 35°, then what is the value of ∠P + ∠C?

Correct — D. The stem is printed as an image: △ABC and △PQR are respectively congruent, with AB = 8 = PQ, BC = 10 = QR and ∠B = 35°.

The letter order fixes the correspondence A↔P, B↔Q, C↔R, so ∠A = ∠P.

Replace ∠P by ∠A and use the angle sum of △ABC:
∠P + ∠C = ∠A + ∠C
= 180° − ∠B
= 180° − 35° = 145° → option (d).

Why the others are wrong

• (a)
  160˚ — 160° would need the marked angle to be 20°, since the other two angles of a triangle total 180° minus it. The image prints 35°.
• (b)
  120˚ — 120° needs a 60° angle at B. The sides 8 and 10 invite a guess at the shape, but the only angle you are given is the 35°.
• (c)
  130˚ — 130° needs 50° at B. The image prints ∠B = 35°, and B is the vertex left out of ∠A + ∠C, so the sum is 180° − 35° = 145°.

Congruent triangles are read letter by letter. Writing △ABC ≅ △PQR is a claim about pairs: A with P, B with Q, C with R.

Every matched part is then equal — that is CPCT, corresponding parts of congruent triangles are equal. So ∠P is simply ∠A wearing a different name.

Once the question is rewritten inside one triangle, the angle sum finishes it. You never need the individual values of ∠A and ∠C, only that together they make 180° − 35°.

Key facts

• In △ABC ≅ △PQR the correspondence is fixed by letter order: A↔P, B↔Q, C↔R.
• CPCT: once two triangles are congruent, every pair of corresponding sides and angles is equal.
• The three angles of a triangle sum to 180°, so one known angle fixes the sum of the other two.
• AB = PQ, BC = QR and the angle between those two sides is the SAS pattern the stem is built on.

Common traps

• Reading △ABC ≅ △PQR as A↔Q or A↔R and pairing the wrong angles
• Chasing ∠A and ∠C separately from the side lengths when only their sum is asked
• Adding the given 35° back into the total after using it

No directly related past PYQ was found.