Hello!
--------------------------------------------------------------------------------------------------------
(a) y = 36° and x = 36°
DAB = 90°
so y = 90° - 54° = 36°
---------------------------------
AB // DC
so x and y are alternate-internal
so x = y = 36°
--------------------------------------------------------------------------------------------------------
(b) y = 73° and x = 68°
SPQ = 90°
so yPQ = 90° - 51° = 39°
the sum of the angles of the triangle PQR = 180°
so y = 180° - (39° + 68°) = 73°
---------------------------------
PSy = 90°
the sum of the angles of the triangle PSy = 180°
so PyS = 180° - (51° + 90°) = 39°
SyxR is a flat angle = 180°
so x = 180° - (39° + 73°) = 68°
--------------------------------------------------------------------------------------------------------
(c) y = 36° and x = 54°
The center of the triangle is K.
So the triangles NKO, MKP, MNK, POK are isosceles
NKO = MKP and MNK = POK
MKP and NKO are opposed
so MKP = NKO = 72°
K is a full angle = 360°
so MKN and PKO = 360° - (72° + 72°) = 216°
so MKN = PKO = 216°/2 = 108°
PMN = y so because MKN is isoscel.
so we know x + y = 90° because PMN = 90°
and so we know PON = OPM = y
and so we know KNO = KON = x
the sum of the angles of the triangle KNO = 180°
so KNO and KON = 180° - 72° = 108°
so x = 108°/2 = 54°
---------------------------------
the sum of the angles of the triangle MKN = 180°
so KMN and KNM = 180° - 108° = 72°
so y = 72°/2 = 36°
--------------------------------------------------------------------------------------------------------