In a rectangle, the diagonals bisect each other, and they also form equal angles where they intersect. You are given that ∠EON = 50° and are asked to find ∠ORT.

Let’s analyze the situation step by step:

1. Since RENT is a rectangle, the diagonals $\overline{RE}$ and $\overline{NT}$ bisect each other at point $O$, meaning $\overline{RO} = \overline{OT}$ and $\overline{EO} = \overline{ON}$.

2. The diagonals of a rectangle divide it into two congruent triangles. So, triangles $\triangle EON$ and $\triangle ROT$ are congruent by the Side-Side-Side (SSS) congruence postulate.

3. Since $\triangle EON$ and $\triangle ROT$ are congruent, corresponding angles are equal. Therefore, $\angle EON = \angle ORT.$

4. From the given information, $\angle EON = 50^\circ$. Thus, $\angle ORT = 50^\circ.$

Therefore, $\angle ORT = 50^\circ$.

---

Would you like more details on the congruence of triangles or any other part of the solution?

Related Questions:

1. How do diagonals behave in a parallelogram compared to a rectangle?
2. If $\overline{RE} = 10$ and $\overline{NT} = 12$, what is the length of $\overline{RO}$?
3. How can you prove that diagonals of a rectangle bisect each other?
4. What is the sum of the interior angles of a rectangle?
5. How do you find the area of a rectangle given the length of its diagonals?

Tip:

In any quadrilateral where diagonals bisect each other, the quadrilateral is always a parallelogram.