Final answer:
The angle of the rhombus formed by the intersection of the diagonals with the sides must be 90°. Since the diagonals intersect at right angles, the only possible answer is option (d) 90°, 90°.
Step-by-step explanation:
The question asks to find the angles of a rhombus where the ratio of the angles formed by diagonals and the sides is 6:5. We know that the diagonals of a rhombus bisect each other at right angles (90°), meaning they form four 90° angles where they intersect. Now, the rhombus has four angles, and the sum of interior angles in any quadrilateral is 360°. Therefore, there are two pairs of congruent angles in the rhombus.
Since the diagonals intersect at a 90° angle, the only possible answer that matches this fact is option (d): 90°, 90°, as it is the only option with right angles. All the other options have angles that are not 90° and thus cannot be formed by the intersection of the diagonals of a rhombus.