1. **Problem statement:** Given that lines AB and CD are parallel, explain why angles $a$ and $d$ are equal, angles $b$ and $e$ are equal, and use these facts to prove that the sum of the angles in triangle ABC is 180°. 2. **Reason why $a = d$:** Since AB and CD are parallel lines cut by a transversal (the vertical line through points A and C), angles $a$ and $d$ are corresponding angles. **Rule:** Corresponding angles formed by a transversal cutting parallel lines are equal. Therefore, $a = d$. 3. **Reason why $b = e$:** Angles $b$ and $e$ are alternate interior angles formed by the transversal cutting the parallel lines AB and CD. **Rule:** Alternate interior angles formed by a transversal cutting parallel lines are equal. Therefore, $b = e$. 4. **Show sum of angles in triangle ABC is 180°:** The triangle ABC has angles $a$, $b$, and the angle at vertex C inside the triangle, which we call angle $c$. At point C on line CD, angles $d$ and $e$ are adjacent and form a straight line, so: $$d + e + c = 180^\circ$$ Using the equalities from steps 2 and 3: $$a + b + c = 180^\circ$$ This shows the sum of the interior angles of triangle ABC is 180°. **Final answer:** The sum of the angles of triangle ABC is 180° because $a = d$, $b = e$, and $d + e + c = 180^\circ$.