Since BCDEF is regular, we know right away that [tex]x=\dfrac{360}5=72[/tex] because the measures of all exterior angles of any regular polygon add to 360 degrees; they are all of equal measure here, so we divide 360 by 5.
For the pentagon BCIHG, the same is true, which means we have the equation
[tex]\underbrace{72}_x+\underbrace{72}_{\angle_{ext}BCD}+\underbrace{90}_{\angle_{ext}CIH}+\underbrace{(180-y)}_{\angle_{ext}IHG}+\underbrace{68}_{\angle_{ext}HGB}=360\implies y=122[/tex]
So [tex]x+y=194[/tex].
