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Right triangle EFG and right triangle EHG overlap as shown below. Angle HEG measures 35° and angle FGE measures 30°.



What are the values of x and y?

Right Triangle EFG And Right Triangle EHG Overlap As Shown Below Angle HEG Measures 35 And Angle FGE Measures 30 What Are The Values Of X And Y class=

Sagot :

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.

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