Notice that the angle with a measure of x is an exterior angle and its remote interior angles are the 46^(∘) and 90^(∘) angles. With this in mind, we can write an equation using the Exterior Angle Theorem for Triangles.
x= 46^(∘)+ 90^(∘)
We can solve this equation for x.
We want to find the value of x. Notice that the 77^(∘) angle corresponds to the angle adjacent to the x angle. Since the two horizontal lines are parallel, the corresponding angles related to these lines and the rightmost vertical line have the same measure. This means that the measure of the angle adjacent to the x angle is 77^(∘).
Notice also that angle x and the 77^(∘) angle form a straight angle, which means that the sum of their measures is 180^(∘). With this in mind, let's write an equation.
x + 77^(∘) = 180^(∘)
We can solve this equation for x. Again, let's ignore the degree symbol to make the math easier.
