Question

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

Answer 1

Given:

Triangle EFG and EHG are two right triangles.

$m\angle HEG=35^\circ$

$m\angle FGE=30^\circ$

To find:

The values of x and y.

Solution:

In triangle EFG,

$m\angle EFG+m\angle FGE+m\angle FEG=180^\circ$        [Angle sum property]

$90^\circ+30^\circ+(x+35)^\circ=180^\circ$

$(x+155)^\circ=180^\circ$

$x+155=180$

$x=180-155$

$x=25$

In triangle EHG,

$m\angle EHG+m\angle HEG+m\angle EGH=180^\circ$        [Angle sum property]

$90^\circ+35^\circ+(y+30)^\circ=180^\circ$

$(y+155)^\circ=180^\circ$

$y+155=180$

$y=180-155$

$y=25$

Therefore, the value of x is 25 and the value of y is also 25.