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if m∠n=42°, then what is m∠k?

The answer to your question is: ∠K   = 138°

Step-by-step explanation:

m∠N = 42°

m∠K = ?

The sum of all the internal angles in a quadrangle equals 360°

then

        ∠N + ∠L + ∠M + ∠K = 360°

        ∠N = ∠ L   and ∠M = ∠K

So, 2 ∠N + 2 ∠K = 360

Substitution

       2 (42) + 2 ∠K = 360

       84  + 2 ∠K = 360

       2 ∠K = 360 - 84

       2 ∠K = 276

      ∠K  = 276 / 2

     ∠K   = 138°