5. a) 7 si 1/3 + 6,(2) + 6 + 7,(8) = 22/3 + 6 si 2/9 + 6 + 7 si 8/9 = 22/3 + 56/9 + 6 + 71/9 = 66/9 + 56/ 9 +54/9 + 71/9 = 247/9 = (243 + 4)/9 = 27 si 4/9 = 27,(4)
b) 8 rad 3 + rad 300 + rad 192 + rad 243 = 8 rad 3 + rad (2^2x3x5^2) + rad (2^6x3) + rad (3^5) = 8 rad 3 + 10 rad 3 + 8 rad 3 + 9 rad 3 = 35 rad 3
7. Formula de calcul este (n-2) x 180 grade
a) n = 4
(n-2) x 180 grade = 2x180 = 360 grade
b) n = 5
(n-2) x 180 grade = 3x180 = 540 grade
Cele 5 unghiuri sunt egale = 540:5 = 108 grade fiecare
c) n = 6
(n-2) x 180 grade = 4 x 180 = 720 grade
Cele 6 unghiuri sunt egale = 720:6 = 120 grade fiecare
d) n = 10
(n-2) x 180 grade = 8 x 180 = 1440 grade
Cele 10 unghiuri sunt egale = 1440:10 = 144 grade fiecare
11. Notam unghiurile cu a, b, c, d
a) a/2 = b/3 = c/4 = d/6 = k
Atunci a = 2k, b= 3k, c = 4k, d = 6k
Dar a+b+c+d = 360
2k+3k+4k+6k = 360
15k = 360
k = 24
Deci a = 48 grade, b= 72 grade, c = 96 grade, d = 144 grade
b) a/2 = b/3 = c/6 = d/7 = k
a = 2k, b = 3k, c = 6k , d = 7k
a+b+c+d = 360
2k+3k+6k+7k = 360
18k = 360
k = 20
a = 40 grade; b = 60 grade; c = 120 grade; d = 140 grade
c) a/6 = b/8 = c/10 = d/12 = k
a = 6k, b = 8k, c = 10k, d = 12k
a+b+c+d = 360
6k + 8k + 10k + 12k = 360
36k = 360
k = 10
Atunci a = 60 grade, b = 80 grade, c = 100 grade, d = 120 grade
