1. **State the problem:** We are given two angles around point K: $\angle JKL = (12x + 3)^\circ$ and $\angle KLM = (6x - 3)^\circ$. We know $\angle JKL$ is a right angle, so it measures $90^\circ$. We need to find the measure of $\angle JKM$. 2. **Use the given information:** Since $\angle JKL$ is a right angle, we have: $$12x + 3 = 90$$ 3. **Solve for $x$:** $$12x = 90 - 3$$ $$12x = 87$$ $$x = \frac{87}{12} = 7.25$$ 4. **Find $\angle KLM$ using $x$:** $$\angle KLM = 6x - 3 = 6(7.25) - 3 = 43.5 - 3 = 40.5^\circ$$ 5. **Find $\angle JKM$:** Since $\angle JKL$ is a right angle and $\angle JKM$ lies between $\angle JKL$ and $\angle KLM$, the sum of $\angle JKM$ and $\angle KLM$ equals $90^\circ$ (because $\angle JKL$ is the right angle at K). So: $$\angle JKM + \angle KLM = 90^\circ$$ $$\angle JKM = 90 - 40.5 = 49.5^\circ$$ **Final answer:** $$m\angle JKM = 49.5^\circ$$