Clock triangle angles

Calculate the sizes of the interior angles in the triangle whose vertices are the points marked by the numbers 1, 5, and 8 on the clock face.

Final Answer:

α =  45 °
β =  60 °
γ =  75 °

Step-by-step explanation:

$$\begin{gathered} \phi =360/12=30{}^{\circ } \\ a=1 \\ b=5 \\ c=8 \\ A=(b-a)\cdot \phi =(5-1)\cdot 30=120{}^{\circ } \\ B=(c-b)\cdot \phi =(8-5)\cdot 30=90{}^{\circ } \\ C=(a-c+12)\cdot \phi =(1-8+12)\cdot 30=150{}^{\circ } \\ \alpha =B/2=90/2=45^{\circ } \end{gathered}$$

$\beta =A/2=120/2=60^{\circ }$

$\gamma =C/2=150/2=75^{\circ }$

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