Given:
Triangle EFG and EHG are two right triangles.
[tex]m\angle HEG=35^\circ[/tex]
[tex]m\angle FGE=30^\circ[/tex]
To find:
The values of x and y.
Solution:
In triangle EFG,
[tex]m\angle EFG+m\angle FGE+m\angle FEG=180^\circ[/tex] [Angle sum property]
[tex]90^\circ+30^\circ+(x+35)^\circ=180^\circ[/tex]
[tex](x+155)^\circ=180^\circ[/tex]
[tex]x+155=180[/tex]
[tex]x=180-155[/tex]
[tex]x=25[/tex]
In triangle EHG,
[tex]m\angle EHG+m\angle HEG+m\angle EGH=180^\circ[/tex] [Angle sum property]
[tex]90^\circ+35^\circ+(y+30)^\circ=180^\circ[/tex]
[tex](y+155)^\circ=180^\circ[/tex]
[tex]y+155=180[/tex]
[tex]y=180-155[/tex]
[tex]y=25[/tex]
Therefore, the value of x is 25 and the value of y is also 25.