1. **Problem Statement:** We need to find the measure of angle 3 in the given rectangle with diagonals intersecting and angles marked. 2. **Understanding the figure:** The rectangle has diagonals intersecting, creating four segments labeled 3, 4, 2, and 1. One angle near the diagonal intersection is 116°, and the rectangle has right angles (90°) at its corners. 3. **Key properties:** - Diagonals of a rectangle are equal in length and bisect each other. - The sum of angles around a point is 360°. - Adjacent angles on a straight line sum to 180°. 4. **Using the given angle:** The angle near the diagonal intersection is 116°. The adjacent angle on the same straight line is: $$180^\circ - 116^\circ = 64^\circ$$ 5. **Finding angle 3:** Since the diagonals bisect each other, the angles formed at the intersection are vertical angles and equal. Angle 3 is vertical to the 64° angle, so: $$\text{angle 3} = 64^\circ$$ 6. **Final answer:** $$\boxed{64^\circ}$$