Question

intr-un triunghi, masurile celor 3 unghiuri ale sale sunt direct proportionale cu numerele 2, 3 si 4. Aflati masurile celor 3 unghiuri

Answer 1

a = 2k

b = 3k

c = 4k

a + b + c = 180

2k + 3k + 4k = 180

9k = 180

k = 20

∡A = 2k = 40°

∡B = 3k = 60°

∡C = 4k = 80°

Answer 2

$\it \{x, y, z \} \: \: d.p \: \: \{2, 3, 4 \} \\ \\ \it \frac{x}{2} = \frac{y}{3} = \frac{z}{4} = K \\ \\ \it \frac{x}{2} = K = = > x = 2K \\ \\ \it \frac{y}{3} = K = = > y = 3K \\ \\ \it \frac{z}{4} = K = = > z = 4K \\ \\ \it x \: + \: y \: + \: z = {180 }^{0} \\ \it 2K \: + \: 3K \: + \: 4K = {180}^{0} \\ \it 9K = {180}^{0} \\ \\ \it K = \frac{180 ^{0} }{9} \\ \\ \it K = {20}^{0} \\ \it x = 2K = = > x = 2 \cdot {20}^{0} = = > \mathbf{x = {40}^{0} } \\ \it y = 3K = = > y = 3 \cdot {20}^{0} = = > \mathbf{ y = 60 ^{0} } \\ \it z = 4K = = > z = 4 \cdot {20}^{0} = = > \mathbf{ z = {80}^{0} }$