The related theorem states that if a quadrilateral has two pairs of parallel sides and one right angle, it is a rectangle. Now, notice that the angles measuring 80^(∘) and x^(∘) are supplementary. This means that their measures add up to 180^(∘).
x^(∘)+80^(∘)=180^(∘)
⇕
x^(∘)=100^(∘)
Also notice that in a rectangle, the bisecting diagonals divide it into four isosceles triangles. Therefore, if we consider the lower triangle with one of the angle measures equal to y^(∘), the other base angle measure is also y^(∘).
The remaining angle is vertical to the 80^(∘) angle, so the two angles are congruent.
To find the value of y^(∘), we apply the Triangle Angle Sum Theorem to this particular triangle. The theorem states that the angle measures of a triangle add up to 180^(∘).
Angle z^(∘) and 50^(∘) are complementary, meaning that their measures add up to 90^(∘).
z^(∘)+50^(∘)=90^(∘) ⇔ z^(∘)=40^(∘)
Now that we have found the value of z^(∘), we can summarize our findings. We found that x^(∘)=100^(∘), y^(∘)=50^(∘), and z^(∘)=40^(∘).
