1. Problem: Find the measures of angles $\alpha$, $\beta$, $\gamma$, and $\delta$ given the values: $\alpha = 138^\circ$ $\beta = 52^\circ$ and $80^\circ$ $\gamma = 65^\circ$ $\delta = 35^\circ$, $38^\circ$, $38^\circ$ 2. Explanation: Angles $\alpha$, $\beta$, $\gamma$, and $\delta$ are given directly or as pairs. When two angles are adjacent and form a straight line, their sum is $180^\circ$. For multiple angles around a point, the sum is $360^\circ$. 3. Calculation: - $\alpha$ is given as $138^\circ$. - $\beta$ has two values $52^\circ$ and $80^\circ$; these likely represent two adjacent angles. - $\gamma$ is $65^\circ$. - $\delta$ has three values $35^\circ$, $38^\circ$, and $38^\circ$; these may be parts of a set of adjacent angles. 4. Interpretation: - Since $\beta$ angles are $52^\circ$ and $80^\circ$, their sum is $52^\circ + 80^\circ = 132^\circ$. - For $\delta$, sum is $35^\circ + 38^\circ + 38^\circ = 111^\circ$. 5. Final answer: - $\alpha = 138^\circ$ - $\beta$ angles are $52^\circ$ and $80^\circ$ - $\gamma = 65^\circ$ - $\delta$ angles are $35^\circ$, $38^\circ$, and $38^\circ$