Question

ayúdenme con estoy por favor, respondan rápido

Answer 1

Respuesta:

Explicación paso a paso:

$\left\lbrace\begin{array}{rcl}\angle{\pi}&=&3x-5^{\circ}\\\\\angle{\alpha}&=&2x\\\\\angle{\beta}&=&4x-15^{\circ}\end{array}\right.$

Por las condiciones anteriores, se obtiene:

$\angle{\pi}+\angle{\alpha}+\angle{\beta}+28^{\circ}+52^{\circ}+75^{\circ}=360^{\circ}\\\\3x-5^{\circ}+2x+4x-15^{\circ}+28^{\circ}+52^{\circ}+75^{\circ}=360^{\circ}\\\\3x+2x+4x=360^{\circ}+5^{\circ}+15^{\cir }-28^{\circ}-52^{\circ}-75^{\circ}\\\\9x=380^{\circ}-155^{\circ}=225^{\circ}\\\\x=\frac{225^{\circ}}{9}\\\\x=25^{\circ}$

Por lo tanto:

$\angle{\pi}=3x-5^{\circ}=3(25^{\circ})-5^{\circ}=70^{\circ}\\\\\angle{\alpha}=2x=2(25^{\circ})=50^{\circ}\\\\\angle{\beta}=4x-15^{\circ}=4(25^{\circ})-15^{\circ}=85^{\circ}$