Answer:
x = 72°
y = 61°
Explanation:
Properties of a kite,
1). At least on pair of opposite angles of a kite are equal.
2). Diagonal of a kite intersect each other at 90°.
3). Diagonals are the angle bisectors of opposite angles.
By these properties,
m∠AED = 90°
In ΔAED,
m∠AED + m∠EDA + m∠DAE = 180° [Triangle sum theorem]
90° + 18° + m∠DAE = 180°
m∠DAE = 180° - 108°
= 72°
Since, diagonal AC is an angle bisector of angle DAB,
x = 72°
In ΔABC,
m∠ABC + m∠BCA + m∠CAB = 180°
m∠ABC + 29° + x° = 180°
m∠ABC + 29° + 72° = 180°
m∠ABC = 180° - 101°
m∠ABC = 79°
Since, opposite angles ∠ADC and ∠ABD are equal in measure,
m∠ABC = m∠ADC = 79°
79° = (18 + y)°
y = 79 - 18
y = 61°