The value of [x] in the figure given is 54.
<h3>What are Alternate interior angles?</h3>
Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal.
Given are two parallel lines.
The two lines are parallel and are intersected by a transversal. Assume
that -
∠1 = (x +3)°
∠2 = (2x - 61)°
Now, the angle at the vertically opposite position with respect to ∠2 will have same measurements. Let's call this ∠3 = (2x - 61)°.
Now, ∠3 and ∠1 are alternate interior angles and their measures will be equal. So, we can write -
∠1 = ∠3
x + 3 = 2x - 61
3 + 61 = 2x - x
x = 64
The value of [x] is 54
Therefore, the value of [x] in the figure given is 54.
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