1. **State the problem:** We have a triangle with three angles: 130°, (x + 5)°, and (x + 15)°. We need to find the value of $x$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of any triangle is always 180°. So, $$130 + (x + 5) + (x + 15) = 180$$ 3. **Set up the equation:** $$130 + x + 5 + x + 15 = 180$$ 4. **Simplify the equation:** $$130 + 5 + 15 + x + x = 180$$ $$150 + 2x = 180$$ 5. **Isolate $x$:** $$2x = 180 - 150$$ $$2x = 30$$ 6. **Solve for $x$:** $$x = \frac{30}{2} = 15$$ 7. **Check the solution:** Calculate the angles: - $x + 5 = 15 + 5 = 20°$ - $x + 15 = 15 + 15 = 30°$ Sum: $130 + 20 + 30 = 180°$, which confirms the solution is correct. **Final answer:** $x = 15$