Explanation:
Hello,
Firstly just look to triangle BDE,
Here, you will find that,
140° = y+80° {the exterior and opposite interior angle of a triangle is equal}.
or, y= 140°-80° {shifting 80° to another side and subtracting it.}
Therefore, the value of y is 60°.
now, let's simply work with line EB or EG. we get;
angle GEF + y=180° { being a linear pair}.
or, angle GEF + 60°= 180°
or, angle GEF = 180°-60°
Therefore, the value of angle GEF = 120°.
now, looking in triangle EFG, we get;
angle GEF + 35°+x= 180° { the sum of interior angle of a triangle is 180°}.
or, 120°+35°+ x= 180°
or, x= 180°- 155°
Therefore, the value of x is 25°.
now, lastly finding the value of "z"
We find that x= z {being vertical opposite angle}
or, z =25°
Therefore, the value of z is 25°.
So, the values are,
x=25°
y=60°
and z= 25°
Hope it helps...