In this triangle the three interior angles are = ∠82° , ∠54° and ∠x .
Then ;
∠82° + ∠54° + ∠x = 180° ( under angle sum property which says that the sum of the three interior angles of a triangle is equal to 180° )
= 136 ° + x = 180
= x = 180 - 136
= x = 44°
∠x and ∠y will sum up to 180° as they are a linear pair .
= 44° + y = 180
= y = 180 - 44
= y = 136°
Since ∠y and ∠z are vertically opposite angles their angle measure will be equal . Which means ;
= ∠y = ∠z
= 136° = ∠z
= ∠z = 136°
Therefore :-
The value of x = 44°