Question

In patrulaterul convex ABCD masurile unghiurilor A,B,C,D sunt direct proportionale cu numerele 2,4,6,8.Determinatu masurile paralelogramului

Answer 1

{ a , b , c , d } d.p { 2 , 4 , 6 , 8 }

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a + b + c + d = 360 °

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a / 2 = b / 4 = c / 6 = d / 8 = K

a / 2 = K => a = 2 K

b / 4 = K => b = 4 K

c / 6 = K => c = 6 K

d / 8 = K => d = 8 K

2 K + 4 K + 6 K + 8 K = 360 °

6 K + 6 K + 8 K = 360 °

12 K + 8 K = 360 °

20 K = 360 °

K = 360° : 20

K = 18

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a = 18 × 2 = 36 °

b = 18 × 4 = 72 °

c = 18 × 6 = 108 °

d = 18 × 8 = 144°