$\alpha ={90}^{\circ }$  

$\delta =\gamma$  

 

$\epsilon +\delta +\gamma =\epsilon +2\delta ={180}^{\circ }$       

 

$\beta ={180}^{\circ }-\alpha -\gamma ={90}^{\circ }-\delta \Rightarrow \delta ={90}^{\circ }-\beta$   

$\beta +\epsilon ={180}^{\circ }$    

$\epsilon ={180}^{\circ }-\beta$      

 

$\epsilon +2\delta ={180}^{\circ }-\beta +2\left({90}^{\circ }-\beta \right)=-3\beta +{360}^{\circ }={180}^{\circ }$      

$3\beta ={180}^{\circ }$  

$\underline{\beta ={60}^{\circ }}$  

$\underline{\gamma +\delta ={60}^{\circ }}$  

$\underline{\epsilon ={180}^{\circ }-\beta ={120}^{\circ }}$  

$\underline{\mu +\alpha =\epsilon ={120}^{\circ }}$