1. **Problem Statement:** We have a rectangle with diagonals drawn, intersecting at the center. We are given that one of the angles formed at the intersection of the diagonals on the right side is 80°. We need to find the measures of angles $\angle 1$ and $\angle 2$. 2. **Important Properties:** - In a rectangle, all angles are 90°. - The diagonals of a rectangle are equal in length and bisect each other. - The diagonals intersect and form vertical angles that are equal. - The sum of angles around a point is 360°. 3. **Analyze the intersection of diagonals:** - The diagonals intersect and form four angles. - Given one angle at the intersection is 80°, the vertical angle opposite it is also 80°. - The other two angles at the intersection are supplementary to 80°, so each is $180° - 80° = 100°$. 4. **Identify angles:** - $\angle 1$ is the bottom angle at the intersection, so it is vertically opposite to the 80° angle, hence $\angle 1 = 80°$. - $\angle 2$ is near the top-right corner of the rectangle, which is a right angle (90°) because it is a corner of the rectangle. 5. **Final answers:** $$\boxed{\angle 1 = 80°}$$ $$\boxed{\angle 2 = 90°}$$