Calculate 11771

The interior angles of the triangle are 108 degrees 45 minutes and 51 degrees 19 minutes. Calculate the outside angle at the third vertex

Correct answer:

C2 =  160.0667 °

Step-by-step explanation:

A = 108 + \dfrac{ 45 }{ 60 } = \dfrac{ 108 \cdot \ 60 }{ 60 } + \dfrac{ 45 }{ 60 } = \dfrac{ 6480 }{ 60 } + \dfrac{ 45 }{ 60 } = \dfrac{ 6480 + 45 }{ 60 } = \dfrac{ 6525 }{ 60 } = \dfrac{ 435 }{ 4 } = 108.75 \ ^\circ \ \\ B = 51 + \dfrac{ 19 }{ 60 } = \dfrac{ 51 \cdot \ 60 }{ 60 } + \dfrac{ 19 }{ 60 } = \dfrac{ 3060 }{ 60 } + \dfrac{ 19 }{ 60 } = \dfrac{ 3060 + 19 }{ 60 } = \dfrac{ 3079 }{ 60 } \doteq 51.3167 \ ^\circ \ \\ \ \\ A+B+C\ = \ 180\degree \ \\ C = 180 - A - B = 180 - \dfrac{ 435 }{ 4 } - \dfrac{ 3079 }{ 60 } = \dfrac{ 299 }{ 15 } \doteq 19.9333 \ ^\circ \ \\ C_{2} = 180 - C = 180 - \dfrac{ 299 }{ 15 } = \dfrac{ 180 \cdot \ 15 }{ 15 } - \dfrac{ 299 }{ 15 } = \dfrac{ 2700 }{ 15 } - \dfrac{ 299 }{ 15 } = \dfrac{ 2700 - 299 }{ 15 } = \dfrac{ 2401 }{ 15 } \doteq 160.0667 \ ^\circ ^\circ \ \\ \ \\ C_{2}\ = \ A+B



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