Clock face

On the circular face of the clock, we connect the points corresponding to the numbers 2, 5, and 9 to each other, which creates a triangle. Calculate the sizes of all interior angles.

Final Answer:

α =  45 °
β =  60 °
γ =  75 °

Step-by-step explanation:

$$\begin{gathered} \phi =360/12=30{}^{\circ } \\ {t}_1=2 \\ {t}_2=5 \\ {t}_3=9 \\ A=(t_2-t_1)\cdot \phi =(5-2)\cdot 30=90{}^{\circ } \\ B=(t_3-t_2)\cdot \phi =(9-5)\cdot 30=120{}^{\circ } \\ C=360-A-B=360-90-120=150{}^{\circ } \\ \alpha =A/2=90/2=45^{\circ } \end{gathered}$$

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

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

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