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Answer 1

∠ A ≅ ∠ E

∠ K = 60°

Explanation:

Part 1.

Given that ABCD ≅ EFGH.

Whenever a quadrilateral is congruent to another, and we write the congruency in symbol, then the order of congruency with respect to angles and sides are maintained in the symbol.

That means if ABCD ≅ EFGH, then ∠ A ≅ ∠ E, ∠ B ≅ ∠ F and so on.

Therefore, in this case, ∠ A ≅ ∠ E (Answer) {It is also shown in the diagrams}

Part 2.

Given that, Δ EFG ≅ Δ KLM

Hence, ∠ E ≅ ∠K, ∠ F ≅ ∠ L, and ∠ G ≅ ∠ M

It is also given that ∠ F = 35° and ∠ G = 85°

So, ∠ E = 180° - ∠ F - ∠ G = 180° - 85° - 35° = 60°

Since, ∠ E = ∠ K,

So, ∠ K = 60°. (Answer)