The $$ m \angle D $$ is supplementary to the $$ m \angle E $$. The $$ m \angle F $$ is supplementary to the $$ m \angle E $$. If $$ m \angle F=113^{\circ} $$, what is the $$ m \angle D $$ and the $$ m \angle E $$ ?

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1. Since $$ m\angle D $$ is supplementary to $$ m\angle E $$, we have:
   $$
   m\angle D + m\angle E = 180^\circ.
   $$

2. Since $$ m\angle F $$ is supplementary to $$ m\angle E $$, we have:
   $$
   m\angle F + m\angle E = 180^\circ.
   $$

3. Substitute the given value $$ m\angle F = 113^\circ $$ into the second equation:
   $$
   113^\circ + m\angle E = 180^\circ.
   $$

4. Solve for $$ m\angle E $$:
   $$
   m\angle E = 180^\circ - 113^\circ = 67^\circ.
   $$

5. Substitute $$ m\angle E = 67^\circ $$ into the first equation:
   $$
   m\angle D + 67^\circ = 180^\circ.
   $$

6. Solve for $$ m\angle D $$:
   $$
   m\angle D = 180^\circ - 67^\circ = 113^\circ.
   $$

Thus, the measures are:
$$
m\angle D = 113^\circ \quad \text{and} \quad m\angle E = 67^\circ.
$$
$$ m\angle D = 113^\circ $$ and $$ m\angle E = 67^\circ $$.

The \( m \angle D \) is supplementary to the \( m \angle E \). The \( m \angle F \) is supplementary to the \( m \angle E \). If \( m \angle F=113^{\circ} \), what is the \( m \angle D \) and the \( m \angle E \) ?

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