1. The problem involves verifying the angle values in a diamond shape inscribed in a circle, with given angles 48°, 48°, 96°, and 84°. 2. First, check the sum of angles in the diamond: $$48^\circ + 48^\circ + 96^\circ + 84^\circ = 276^\circ$$ which is incorrect because the sum of interior angles in any quadrilateral must be $$180^\circ \times 2 = 360^\circ$$. 3. The sum 276° is less than 360°, so the given angles cannot form a diamond (a quadrilateral). 4. Next, check the calculations: - $$90^\circ - 42^\circ = 48^\circ$$ correct. - $$48^\circ + 48^\circ = 96^\circ$$ correct. - $$180^\circ - 96^\circ = 84^\circ$$ correct. - $$42^\circ + 84^\circ = 126^\circ$$ correct. - $$180^\circ - 126^\circ = 54^\circ$$ correct. 5. The value of $$x = 54^\circ$$ is consistent with the calculations. 6. The value of $$y = 48^\circ$$ is also consistent. 7. Conclusion: The individual angle calculations are correct, but the sum of the diamond's angles is incorrect for a quadrilateral. Therefore, the diamond angle values as given are wrong for a quadrilateral. Final answer: The calculations for $$x$$ and $$y$$ are right, but the diamond's angle sum is wrong and cannot form a valid quadrilateral.