Explicație pas cu pas:
a)
[tex]3x - 10 + 3x + x + 28 = 180 \\ 7x + 18 = 180 \\ 7x = 162 = > x = \frac{162}{7} [/tex]
[tex]\hat A = 3 \times \frac{162}{7} - 10 = \frac{416}{7} \approx59.5\degree \\ [/tex]
[tex]\hat B = 3 \times \frac{162}{7} = \frac{486}{7} \approx 69.5\degree \\ [/tex]
[tex]\hat C = \frac{162}{7} + 28 = \frac{358}{7} \approx51 \degree \\ [/tex]
b)
[tex]x + 40 + 2x - 15 + x - 3 = 180 \\ 4x + 22 = 180 < = > 4x = 158 \\ = > x =39.5 [/tex]
[tex]\hat A = 39.5 + 40 = 79.5 \degree \\ [/tex]
[tex]\hat B = 2 \times 39.5 - 15 = 79 - 15 = 64 \degree \\ [/tex]
[tex]\hat C = 39.5 - 3 = 36.5 \degree \\ [/tex]
c)
[tex]x - 1 + 3x - 3 + 2x - 2 = 180 \\ 6x - 6 = 180 < = > 6x = 180 + 6 \\ 6x = 186 = > x = 31[/tex]
[tex]\hat A = 31 - 1 = 30\degree \\ [/tex]
[tex]\hat B = 3 \cdot 31 - 3 = 93 - 3 = 90\degree \\ [/tex]
[tex]\hat C = 2 \cdot 31 - 2 = 62 - 2 = 60\degree \\ [/tex]
