Question

Can you help me how to solve this problem ? thank you

Answer 1

Since BCDEF is regular, we know right away that $x=\dfrac{360}5=72$ 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

$\underbrace{72}_x+\underbrace{72}_{\angle_{ext}BCD}+\underbrace{90}_{\angle_{ext}CIH}+\underbrace{(180-y)}_{\angle_{ext}IHG}+\underbrace{68}_{\angle_{ext}HGB}=360\implies y=122$

So $x+y=194$.