Special watch

Fero bought a special watch on the market. They have only one (minute) hand and a display that shows which angle between the hour and minute hand. How many hours was his watch shown - the minute hand points to number 2; the display shows 125°?

Result

h₁ = 6:10
h₂ = 9:50

Step-by-step explanation:

$$\begin{gathered} d={\displaystyle \frac{360}{12}}=30^{\circ } \\ A=125^{\circ } \\ B=360-A=360-125=235^{\circ } \\ {m}_1=2\cdot d=2\cdot 30=60^{\circ } \\ {h}_1=(A+m_1)\mathrm{/}d=(125+60)\mathrm{/}30={\displaystyle \frac{37}{6}}=6\frac{1}{6}=6.16667=6:10 \end{gathered}$$

$$\begin{gathered} h_2=(B+m_1)\mathrm{/}d=(235+60)\mathrm{/}30={\displaystyle \frac{59}{6}}=9\frac{5}{6}\doteq 9.8333=9.83333=9:50 \\ {h}_2\dots nevyhovuje \end{gathered}$$

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