We will start by analyzing the given figure. Let's name the angle adjacent to the angle measuring x^(∘) as y.
First, we will find the value of y and then use it to find x. Let's do those things one at a time.
Value of y
Let's take a look at the given diagram once again.
Notice that the angle whose measure is y and the angle with measure 75 are alternate angles. The Alternate Interior Angles Theorem tells us that alternate angles formed by parallel lines and a transversal are congruent. Therefore, these angles are congruent and their measures are the same.
y= 75
Value of x
Let's add the obtained information to the diagram.
Notice that the angles which measure x^(∘), 45^(∘), and 75^(∘) are adjacent angles and by the Same-Side Interior Angles Postulate form an angle which measures 180^(∘).
