Clock hands

Calculate the internal angles of a triangle whose vertices lie on the clock's 2, 6 and 11 hours.

Correct answer:

A =  75 °
B =  60 °
C =  45 °

Step-by-step explanation:

$$\begin{gathered} \phi =360\mathrm{/}12=30\text{ ° } \\ \alpha =(6-2)\cdot \phi =(6-2)\cdot 30=120\text{ ° } \\ \beta =(11-6)\cdot \phi =(11-6)\cdot 30=150\text{ ° } \\ \gamma =(2+12-11)\cdot \phi =(2+12-11)\cdot 30=90\text{ ° } \\ A=\beta \mathrm{/}2=150\mathrm{/}2=75\text{°} \end{gathered}$$

$B=\alpha \mathrm{/}2=120\mathrm{/}2=60\text{°}$

$C=\gamma \mathrm{/}2=90\mathrm{/}2=45\text{°}$

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