Respuesta :
We know that
[tex]m\angle\text{BYD}+m\angle\text{DYO}=m\angle\text{BYO}[/tex]Then, let's put the respective equation and values:
[tex]\begin{gathered} m\angle\text{BYD}+m\angle\text{DYO}=m\angle\text{BYO} \\ \\ (x+4)+(3x-8)=68\degree \end{gathered}[/tex]Now we solve the equation for x
[tex]\begin{gathered} (x+4)+(3x-8)=68 \\ \\ x+4+3x-8=68 \\ \\ x+3x=68+8-4 \\ \\ 4x=72 \\ \\ x=18 \end{gathered}[/tex]Therefore the value of x is 18.
Now we have the value of x we can find out m∠DYO:
[tex]\begin{gathered} m\angle\text{DYO}=3x-8 \\ \\ m\angle\text{DYO}=3\cdot(18)-8 \\ \\ m\angle\text{DYO}=54-8 \\ \\ m\angle\text{DYO}=46\degree \end{gathered}[/tex]Hence, m∠DYO = 46°
The final answers are
x = 18
m∠DYO = 46°
