Quadrilateral with two pairs of consecutive congruent sides and no opposite congruent sides.
Diagonals are perpendicular.
Now let's take a look at the given figure.
In the given quadrilateral, exactly one pair of opposite sides is parallel. We also see that two of its sides are congruent. Therefore, the figure is an isosceles trapezoid. We know from the table that for this figure, the base angles have the same measure.
We also know that in an isosceles trapezoid, a lower base angle and its consecutive upper base angle are supplementary, meaning they add up to 180^(∘). We can use this fact to find the value of x^(∘).
50^(∘)+x^(∘)=180^(∘) ⇒ x^(∘)=130^(∘)
We found that x^(∘)=130^(∘) and y^(∘)=50^(∘).
