Explanation:
the diagonals in a square are intersecting each other at 90°.
that means that G1 + G2 = 90
and because of the symmetry of a kite, it also means that G1 = G2.
combined this tells us
G1 = G2 = 90/2 = 45°.
also due to its symmetry one of the rules of a kite is that its diagonals are also intersecting each other at 90°.
so,
E1 = E2 = 90°.
the sum of all angles in a triangle is always 180°.
so,
180 = F1 + G1 + (D2 + D3) = F1 + 45 + 110
F1 = 180 - 45 - 110 = 180 - 155 = 25°
again, due to the symmetry of the kite
F1 = F2 = 25°.
also
C2 + C3 = D2 + D3 = 110°
due to the properties of a square (e.g. the angle in every corner is 90°, the diagonals are splitting each corner angle in half) we know that
D1 = D2 = 45°.
and again, therefore
C1 = C2 = D1 = D2 = 45°
and so
(1)
due to the law of the angles of a line intersecting parallel lines are equal for every parallel line, we see that
the line BD intersects the lines AD and GEF equally at 45°. therefore, GEF || AD.
(2)
as we know that F1 = F2 = 25°,
F1 + F2 = 2×25 = 50°
(3)
the angles in the triangle GDE are
E1 = 90°
D2 = 45°
G1 = 45°
the angles of GE and DE with their baseline GD are equal, that means this is an isoceles triangle, meaning the legs have an identical length, and therefore
DE = GE.
(4)
as GDE is a right-angled triangle we can use Pythagoras :
GD² = GE² + DE² = 2×DE² = 2×GE²
GD = 3×sqrt(2)
GD² = 9×2 = 18
18 = 2×DE² = 2×GE²
DE² = GE² = 18/2 = 9
DE = GE = 3