Quadrilateral 8405

Calculate the magnitude of the largest inner angle and the deviation of the diagonals in the quadrilateral, whose vertices correspond to points 1, 5, 8, and 12 on the dial.

Correct answer:

X =  105 °
U =  0 °

Step-by-step explanation:

$$\begin{gathered} d=360/12=30{}^{\circ } \\ {x}_1=(5-0)\cdot d/2=(5-0)\cdot 30/2=75{}^{\circ } \\ {x}_5=(8-1)\cdot d/2=(8-1)\cdot 30/2=105{}^{\circ } \\ {x}_8=(12-5)\cdot d/2=(12-5)\cdot 30/2=105{}^{\circ } \\ {x}_{12}=(13-8)\cdot d/2=(13-8)\cdot 30/2=75{}^{\circ } \\ X=\max (x_1,x_5,x_8,x_{12})=\max (75,105,105,75)=105^{\circ } \end{gathered}$$

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