1. **Stating the problem:** Find the value of $x$ in the triangle where the angles are given as $(9x + 8)^\circ$, $(10x)^\circ$, and $(8x + 10)^\circ$ and their sum is $180^\circ$. 2. **Formula used:** The sum of the interior angles of any triangle is always $180^\circ$. So, $$ (9x + 8) + 10x + (8x + 10) = 180 $$ 3. **Combine like terms:** $$ 9x + 8 + 10x + 8x + 10 = 180 $$ $$ (9x + 10x + 8x) + (8 + 10) = 180 $$ $$ 27x + 18 = 180 $$ 4. **Isolate $x$:** $$ 27x = 180 - 18 $$ $$ 27x = 162 $$ 5. **Divide both sides by 27:** $$ x = \frac{162}{27} $$ $$ x = \cancel{\frac{162}{27}} \Rightarrow x = 6 $$ **Final answer:** $x = 6$. 1. **Stating the problem:** Find the value of $x$ in the right triangle where the angles are $(20x - 9)^\circ$, $90^\circ$, and $(10x + 9)^\circ$ and their sum is $180^\circ$. 2. **Formula used:** The sum of the interior angles of any triangle is $180^\circ$. So, $$ (20x - 9) + 90 + (10x + 9) = 180 $$ 3. **Combine like terms:** $$ 20x - 9 + 90 + 10x + 9 = 180 $$ $$ (20x + 10x) + (-9 + 90 + 9) = 180 $$ $$ 30x + 90 = 180 $$ 4. **Isolate $x$:** $$ 30x = 180 - 90 $$ $$ 30x = 90 $$ 5. **Divide both sides by 30:** $$ x = \frac{90}{30} $$ $$ x = \cancel{\frac{90}{30}} \Rightarrow x = 3 $$ **Final answer:** $x = 3$.