Question

PLEASE HELP!! find x and y

Answer 1

Answer:

x = 72°

y = 61°

Step-by-step 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°