Given: $$ r \| $$ s; $$ m \angle 1=29^{\circ} ; m \angle 15=65 $$

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Given:
- $$ r \parallel s $$
- $$ m \angle 1 = 29^{\circ} $$
- $$ m \angle 15 = 65^{\circ} $$

Since $$ r \parallel s $$, we know that corresponding angles are equal. Therefore, $$ m \angle 1 = m \angle 15 $$.

We are given that $$ m \angle 1 = 29^{\circ} $$ and $$ m \angle 15 = 65^{\circ} $$. However, these angles are not corresponding angles, so we cannot directly conclude that $$ r \parallel s $$ based on the given information.

To determine if $$ r \parallel s $$, we need to find the measure of the angle between $$ r $$ and $$ s $$. Let's call this angle $$ x $$. Since $$ m \angle 1 = 29^{\circ} $$ and $$ m \angle 15 = 65^{\circ} $$, we can find the measure of angle $$ x $$ using the fact that the sum of the interior angles of a triangle is 180 degrees.

Let's calculate the measure of angle $$ x $$ using the given information.
Calculate the value by following steps:
- step0: Calculate:
  $$29+65$$
- step1: Add the numbers:
  $$94$$
The measure of angle $$ x $$ is 94 degrees.

Since the sum of the interior angles of a triangle is 180 degrees, we can set up the equation:
$$ 29 + 65 + x = 180 $$

Solving for $$ x $$, we get:
$$ x = 180 - 29 - 65 $$
$$ x = 86 $$

Therefore, the measure of angle $$ x $$ is 86 degrees.

Since the measure of angle $$ x $$ is not equal to 0 degrees, we can conclude that $$ r $$ and $$ s $$ are not parallel.
$$ r $$ and $$ s $$ are not parallel.

Given: s;

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