Answer:
[tex]\angle AFY=140^\circ[/tex]
[tex]\angle LIM=117^\circ[/tex]
Step-by-step explanation:
The sum of interior angles of a polygon of n sides is:
[tex]S=180^\circ (n-2)[/tex]
The image shows a 6-side polygon. The sum of the interior angles is:
[tex]S=180^\circ (6-2)=720^\circ[/tex]
The sum of all the shown interior angles must equal 900°:
[tex]125+100+y+117+121+y+23=720[/tex]
Simplifying:
[tex]486+2y=720[/tex]
Solving:
[tex]2y=720-486[/tex]
[tex]2y=234[/tex]
[tex]y=234 / 2=117[/tex]
y=117°
Thus the angle AFY is:
[tex]\angle AFY=y+23=117+23=140[/tex]
[tex]\boxed{\angle AFY=140^\circ}[/tex]
[tex]\angle LIM=y=117[/tex]
[tex]\boxed{\angle LIM=117^\circ}[/tex]
