complementary angles $$ A $$ and $$ B $$, where $$ m \angle A=(y-16)^{\circ} $$ and $$ m \angle B=(y+4)^{\circ} $$

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1. Since complementary angles add up to $$90^\circ$$, we have
   $$
   (y - 16) + (y + 4) = 90.
   $$

2. Combine like terms:
   $$
   2y - 12 = 90.
   $$

3. Add $$12$$ to both sides:
   $$
   2y = 102.
   $$

4. Divide both sides by $$2$$:
   $$
   y = 51.
   $$

5. Now, substitute $$y = 51$$ into the expressions for the angles:
   $$
   m \angle A = 51 - 16 = 35^\circ,
   $$
   $$
   m \angle B = 51 + 4 = 55^\circ.
   $$

6. Verification:
   $$
   35^\circ + 55^\circ = 90^\circ.
   $$

Therefore, the measures of the complementary angles are $$35^\circ$$ and $$55^\circ$$.
The measures of the complementary angles are $$35^\circ$$ and $$55^\circ$$.

complementary angles \( A \) and \( B \), where \( m \angle A=(y-16)^{\circ} \) and \( m \angle B=(y+4)^{\circ} \)

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