Angle X 6A3C82

1. **Problem Statement:** We are given a quadrilateral with two diagonals intersecting at a right angle (90°). One angle formed between the base and a diagonal is 30°, and we need to find the value of $x$ (another angle in the figure). 2. **Understanding the problem:** The diagonals intersect at 90°, and one angle adjacent to the base is 30°. We want to find $x$, which is the angle opposite or related to these given angles. 3. **Key properties:** In a parallelogram, the diagonals bisect each other. The angles around the intersection of diagonals add up to 360°, and since one angle is 90°, the adjacent angles relate accordingly. 4. **Using angle sum properties:** Since the diagonals intersect at 90°, the angles around the intersection are $90°$, $90°$, $x°$, and $x°$ (because opposite angles are equal). 5. **Calculate $x$:** The sum of angles around the intersection is $$90° + 90° + x + x = 360°$$ 6. Simplify: $$180° + 2x = 360°$$ 7. Subtract 180° from both sides: $$\cancel{180°} + 2x = 360° - \cancel{180°}$$ $$2x = 180°$$ 8. Divide both sides by 2: $$\frac{2x}{\cancel{2}} = \frac{180°}{\cancel{2}}$$ $$x = 90°$$ 9. **Final answer:** $$\boxed{90°}$$ Thus, the value of $x$ is $90°$.