well, as we can see from the tickmarks on the slanted sides, they're equal, meaning is an isosceles trapezoid, meaning the angles up above are equal to each other, and the angles down below are also equal to each other, namely.
z = y and 5x + 45 = 20x.
[tex]\bf 5x+45=20x\implies 45=15x\implies \cfrac{45}{15}=x\implies \boxed{3=x} \\\\\\ 5x+45\implies 5(3)+45\implies \blacktriangleright 60 \blacktriangleleft\impliedby 20x[/tex]
well, the sum of all interior angles in a polygon is
180(n - 2), where n = sides
this trapezoid has 4 sides, so the sum of all its interior angles is 180(4 - 2) = 360°.
well, we know that the angles above are 60° each, so that's 120° for those, and 360° - 120° = 240°, so "z" and "y" will evenly split 240°, namely ∡z = ∡y = 120°.
