1. **State the problem:** We have a triangle SQT with angles $S=113^\circ$, $Q=4x$, and $T=6x+3$. We need to find the values of $x$ and the angles $Q$ and $T$. 2. **Use the triangle angle sum rule:** The sum of the interior angles of a triangle is always $180^\circ$. 3. **Set up the equation:** $$113 + 4x + (6x + 3) = 180$$ 4. **Simplify the equation:** $$113 + 4x + 6x + 3 = 180$$ $$113 + 10x + 3 = 180$$ $$10x + 116 = 180$$ 5. **Isolate $x$:** $$10x = 180 - 116$$ $$10x = 64$$ 6. **Divide both sides by 10:** $$\cancel{10}x = \frac{64}{\cancel{10}}$$ $$x = 6.4$$ 7. **Find angles $Q$ and $T$:** $$Q = 4x = 4 \times 6.4 = 25.6^\circ$$ $$T = 6x + 3 = 6 \times 6.4 + 3 = 38.4 + 3 = 41.4^\circ$$ 8. **Check the sum:** $$113 + 25.6 + 41.4 = 180^\circ$$ **Final answer:** $$x = 6.4$$ $$Q = 25.6^\circ$$ $$T = 41.4^\circ$$