Question

Plantear la ecuación y hallar los ángulos desconocidos.

paso a paso plis​

Answer 1

Respuesta:

a.

$\Rightarrow \alpha + \beta + \gamma = 180° \\ 6x + 14x + 10x = 180 \\ 30x = 180° \\ x = \frac{180°}{30} \\ \boxed{x = 6 ° }$

$\alpha = 6x \\ \alpha =( 6)(6°) \Rightarrow \: \alpha = 36° \\ \\ \beta = 14x \\ \beta (14)(6°)\Rightarrow \beta = 84° \\ \\ \gamma = 10x \\ \gamma = (10)(6°)\Rightarrow \gamma = 60°$

b.

$\Rightarrow \beta + \varphi = 90° \\ 3x + 13° + 2x + 2° = 90° \\ 5x + 15° = 90° \\5x = 90° - 15° \\ 5x = 75° \\ x = \frac{75°}{5} \\ \boxed{ x = 15°}$

$\beta = 3x + 13° \\ \beta (3)(15°) + 13°\Rightarrow \beta = 58° \\ \\ \varphi = 2x + 2° \\ \varphi = (2)(15°) + 2° \Rightarrow \varphi = 32°$

c.

$\Rightarrow \alpha = \delta \\ 3x + 30° = x + 110° \\ 3 x - x = 110° - 30° \\ 2x = 80° \\ x = \frac{80°}{2} \\ \boxed {x = 40°}$

$\alpha = 3x + 30° \\ \alpha = 3(40°) + 30° \Rightarrow \alpha = 150° \\ \\ \delta = x + 110° \\ \delta= 40° + 110°\Rightarrow \delta = 150°$

d.

$\Rightarrow \alpha + \varphi = 180° \\ 2x + 5° + 6x + 15° = 180° \\8x + 20° = 180° \\ 8x = 180° - 20°\\ 8x = 160° \\ x = \frac {160°}{8} \\ \boxed{x = 20°}$

$\alpha = 2x + 5° \\ \alpha (2)(20°) + 5°\Rightarrow \alpha = 45° \\ \\ \varphi = 6x + 15° \\ \varphi = (6)(20°) + 15° \Rightarrow \varphi = 135°$

Como tambien:

$\large{\boxed{\mathsf{\varphi = \delta}}}$

Answer 2

Respuesta:

gracias por la respuesta correcta