1. The problem is to show that the angles in a triangle sum to 180° using angle facts. 2. We start by drawing a triangle with angles labeled $x$, $y$, and $z$. 3. Next, draw a line parallel to the base of the triangle above it. 4. At step 3, we mark angle $x$ on the straight line using the fact that \textbf{alternate interior angles are equal} (A). 5. At step 4, we mark angle $y$ on the straight line using the fact that \textbf{alternate interior angles are equal} (B). 6. At step 5, using the fact that \textbf{angles on a straight line sum to 180°} (C), we conclude that $x + y + z = 180^\circ$, so the angles in a triangle sum to 180°. This completes the proof.