Show for which real number x and y it is true that ⌈x + y⌉ = ⌈x⌉ + ⌈y⌉?

In trapezoid efgh, m∠hef=(4x2+16)∘ and m∠gfe=(5x2+12)∘. find the value of x so that efgh is isosceles. i'm desperate.

In the figure below, ∠dec ≅ ∠dce, ∠b ≅ ∠f, and segment df is congruent to segment bd. point c is the point of intersection between segment ag and segment bd, while point e is the point of intersection between segment ag and segment df. the figure shows a polygon comprised of three triangles, abc, dec, and gfe. prove δabc ≅ δgfe.

What is the image of c for a 90° counterclockwise rotation about a? (3, 7) (-1, 3) (7, 3)