1. **State the problem:** We are given three rays originating from point N: NL, NK, and NM. The angles are: - Angle between NK and NL is 42° - Angle between NL and NM is 89° - Angle between NK and NM is labeled as (10x - 3)° 2. **Use the angle sum rule:** The three rays form a full circle around point N, so the sum of the angles between them is 360°. 3. **Set up the equation:** $$42 + 89 + (10x - 3) = 360$$ 4. **Simplify the equation:** $$42 + 89 = 131$$ So, $$131 + 10x - 3 = 360$$ $$10x + 128 = 360$$ 5. **Isolate $x$:** $$10x = 360 - 128$$ $$10x = 232$$ 6. **Solve for $x$:** $$x = \frac{232}{10}$$ $$x = 23.2$$ **Final answer:** $$x = 23.2$$