Question

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

Answer 1

Since BCDEF is regular, we know right away that
`x=\frac{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`.