1. **State the problem:** We need to find the unknown angle $x$ in three different triangles given the other angles. 2. **Recall the rule:** The sum of the interior angles in any triangle is always $180^\circ$. So, for any triangle with angles $a$, $b$, and $c$, we have: $$a + b + c = 180^\circ$$ 3. **Solve for each triangle:** **Triangle 1:** Given angles $38^\circ$ and $23^\circ$, find $x$. $$x + 38 + 23 = 180$$ $$x + 61 = 180$$ $$x = 180 - 61$$ $$x = 119^\circ$$ **Triangle 2:** Given angles $40^\circ$ and $115^\circ$, find $x$. $$x + 40 + 115 = 180$$ $$x + 155 = 180$$ $$x = 180 - 155$$ $$x = 25^\circ$$ **Triangle 3:** Given angles $11^\circ$, $75^\circ$, and $48^\circ$, find $x$. $$x + 11 + 75 + 48 = 180$$ $$x + 134 = 180$$ $$x = 180 - 134$$ $$x = 46^\circ$$ **Final answers:** - Triangle 1: $x = 119^\circ$ - Triangle 2: $x = 25^\circ$ - Triangle 3: $x = 46^\circ$