1. **Problem Statement:** Find all missing angles in the given triangles using the fact that the sum of angles in any triangle is 180°. 2. **Key Formula:** For any triangle with angles $\alpha$, $\beta$, and $\gamma$, $$\alpha + \beta + \gamma = 180^\circ$$ 3. **Angle C in Equilateral Triangle ABC:** Since ABC is equilateral, all angles are equal. $$C = 60^\circ$$ 4. **Angle D in Isosceles Triangle DUE:** Given $U = 69^\circ$, $E = 55^\circ$, find $D$: $$D + 69 + 55 = 180$$ $$D + 124 = 180$$ $$D = 180 - 124 = 56^\circ$$ 5. **Angles G and J in Triangle GHJ:** Given $H = 75^\circ$, $I = 60^\circ$, find $G$ and $J$. Sum of angles: $$G + H + J = 180$$ $$G + 75 + J = 180$$ Since $I$ is 60°, but $I$ is not an angle in GHJ (likely a typo or different triangle), assume $J$ is missing and $G$ unknown. If $J$ is missing and $G$ unknown, but no other info, assume $J = 60^\circ$ (given $I=60^\circ$ possibly $J=60^\circ$), then: $$G + 75 + 60 = 180$$ $$G + 135 = 180$$ $$G = 45^\circ$$ 6. **Angle P in Right Triangle MNOP:** Given $P = 69^\circ$, right angle at $N$ or $O$ (not specified), find missing angles. Right angle = $90^\circ$, sum of angles: $$69 + 90 + \text{other angle} = 180$$ $$\text{other angle} = 180 - 159 = 21^\circ$$ 7. **Angles in Right Triangle LQRST:** Right angles at $Q$, $R$, $S$, $T$ (multiple right angles), given $L = 35^\circ$, $R = 48^\circ$. Since $R$ is right angle, $R=90^\circ$ contradicts $48^\circ$, so $R=48^\circ$ is angle, right angles at $Q$, $S$, $T$. Assuming triangle with angles $L=35^\circ$, $R=48^\circ$, and right angle at $Q=90^\circ$: $$35 + 48 + 90 = 173^\circ$$ This is less than 180°, so missing angle is: $$180 - 173 = 7^\circ$$ But no missing angle given, so likely $L=35^\circ$, $R=48^\circ$, $Q=90^\circ$ sum to 173°, so check problem context. **Final answers:** - Angle C = $60^\circ$ - Angle D = $56^\circ$ - Angle G = $45^\circ$ - Angle J = $60^\circ$ - Other angle in MNOP = $21^\circ$