The image presents a scenario where two parallel lines are cut by a transversal, and it asks which statement is true about the measure of angle $x$. The angles formed involve one given as $127^\circ$.

Let's analyze:

1. The given angle is $127^\circ$. This angle and $x^\circ$ are supplementary because they form a linear pair (they are adjacent on a straight line). Supplementary angles add up to $180^\circ$.

   Therefore: $x^\circ + 127^\circ = 180^\circ$ $x^\circ = 180^\circ - 127^\circ = 53^\circ$

Now, we examine the statements given in the multiple choices:

• "m∠x = 53° because alternate interior angles are congruent."
• "m∠x = 53° because corresponding angles are congruent."
• "m∠x = 53° because same side exterior angles are supplementary."
• "m∠x = 53° vertical angles are congruent."

The correct answer is:

"m∠x = 53° because same side exterior angles are supplementary." This is true since $x^\circ$ and the given $127^\circ$ are on the same side of the transversal and exterior to the parallel lines, making them supplementary.

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. What are alternate interior angles, and when are they congruent?
2. Can vertical angles ever be supplementary?
3. How do you determine corresponding angles when a transversal cuts parallel lines?
4. What is the general rule for same-side interior and exterior angles?
5. Why do supplementary angles always add up to $180^\circ$?

Tip: When working with angles formed by a transversal and parallel lines, identifying the relationship (alternate, corresponding, or supplementary) can quickly help find unknown angles.