..Step by step explanation..
1.
let the interior angles of the given triangle be angle a b c respectively.
116+a=180 (Sum of angles on a straight line.)
a=180-116
a=64
.......
112+b=180(Sum of angles on a straight line.)
Sum of angles on a straight line.)b=180-112
b=68
....
angle a +b+c=180 (Sum of angles of a triangle)
64+68+c=180
c=180-132
c=48
.,....
angle c +X =180(Sum of angles on a straight line.)
48+X=180
X=132
Therefore the value of X is 132.
2.
solution,
Let the remaining interior angle of the given triangle be y.
Then,
y+108=180(Sum of angles on a straight line.)
y=72
Again,
2x+X+y=180(Sum of angles of a triangle)
3x+72=180
3x=108
X=108÷3
X=36
Therefore the value of X is 36.
3.
solution,
let the remaining interior angle of the given polygon be a and b .
Then,
100+b=180(Sum of angles on a straight line.)
b=80
......
Again,
a+b+110+90=360(Sum of interior angle of the polygon)
a+80+200=360
a+280=360
a=80
.....
a+X=180(Sum of angles on a straight line.)
80+X=180
X=100
Therefore the value of X is 100.
4.
solution,
The given triangle is an isosceles triangle.So their base angles are equal .
43+43+X=180(Sum of angles of a triangle)
X=180-86
X=94
Therefore the value of X is 94.
5.
solution,
Opposite angles of a parallelogram is equal
So ,
X=125
Therefore the value of X is 125.
6.
solution,
Let the remaining interior angle of the triangle be a .
Then,
a+117=180 (Sum of angles on a straight line.)
a=63
Now,
a+X+83=180(Sum of angles of a triangle)
63+83+X=180
146+X=180
X=34
Therefore ,the value of X is 34.
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