We want to find the value of x. First, we will label two of the angles. We will give the name y to the angle next to angle x. The angle created by the intersection of the lines b and d will be z. Let's take a look at the given picture and add the assigned labels.
They lie between the two lines on opposite sides of the transversal.
We know that alternate interior angles are only congruent if the lines cut by the transversal are parallel. Notice that, in this picture, lines c and d are parallel and line b is a transversal. We can see that the 50^(∘) angle and angle z are alternate interior angles. Because of this, the measure of angle z is 50^(∘). Let's add this information to our diagram.
Next, we will use the fact that lines a and b are parallel and cut by a transversal d. We can see that the 50^(∘) angle and angle y are corresponding angles. Corresponding angles are congruent so the measure of angle y is also 50^(∘).
The 50^(∘) angle and angle x form a straight line, which means that they are supplementary angles. Therefore, their measures add up to 180^(∘).
x^(∘)+ 50^(∘)=180^(∘) ⇕ x^(∘)= 130^(∘)
We found that the value of x is 130.
