Gamma angle

Find the magnitude of the gamma angle in triangle ABC if: α = 38° 56 ’and β = 47° 54’.

Correct answer:

C =  93.1667 °

Step-by-step explanation:

$$\begin{gathered} A=38{\displaystyle \frac{56}{60}}={\displaystyle \frac{38\cdot 60+56}{60}}={\displaystyle \frac{2336}{60}}={\displaystyle \frac{584}{15}}\doteq 38.9333^{\circ } \\ B=47{\displaystyle \frac{54}{60}}={\displaystyle \frac{47\cdot 60+54}{60}}={\displaystyle \frac{2874}{60}}={\displaystyle \frac{479}{10}}=47.9^{\circ } \\ A+B+C=180^{\circ } \\ C=180-A-B=180-38.9333-47.9={\displaystyle \frac{559}{6}}=93.1667^{\circ }=93^{\circ }10^{\mathrm{\prime }} \end{gathered}$$

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