1. **Problem:** Given that □ROCK is a rhombus, and angles m∠KCR = 7x - 9 and m∠OCR = 5x + 5, find the value of $x$. 2. **Understanding the problem:** In a rhombus, the diagonals bisect each other at right angles. This means the diagonals intersect at 90°. 3. **Formula and theorem used:** Since diagonals are perpendicular, the sum of the angles formed by the diagonals at the intersection point is 90°. 4. **Set up the equation:** $$ (7x - 9) + (5x + 5) = 90 $$ 5. **Simplify the equation:** $$ 7x - 9 + 5x + 5 = 90 $$ $$ 12x - 4 = 90 $$ 6. **Solve for $x$:** $$ 12x = 90 + 4 $$ $$ 12x = 94 $$ $$ x = \frac{94}{12} = 7.8333... $$ 7. **Adjusting for a whole number:** Since the user requested a whole number, check if rounding $x$ to 8 works: Calculate angles with $x=8$: $$ m\angle KCR = 7(8) - 9 = 56 - 9 = 47 $$ $$ m\angle OCR = 5(8) + 5 = 40 + 5 = 45 $$ Sum: $47 + 45 = 92$, which is close but not exactly 90. Try $x=7$: $$ m\angle KCR = 7(7) - 9 = 49 - 9 = 40 $$ $$ m\angle OCR = 5(7) + 5 = 35 + 5 = 40 $$ Sum: $40 + 40 = 80$, less than 90. Try $x=7.5$ (not whole number but closer): $$ 7(7.5) - 9 = 52.5 - 9 = 43.5 $$ $$ 5(7.5) + 5 = 37.5 + 5 = 42.5 $$ Sum: $43.5 + 42.5 = 86$, still less than 90. Since exact whole number solution is not possible, the closest whole number is $x=8$. **Final answer:** $x = 8$ (approximate whole number solution).