Question

ABCD is a kite .Find the angles marked x and y in the given figure.​

Answer 1

Answer:

x = 72°

y = 61°  

Step-by-step explanation:

In the above triangle Δ ABD

Angle B = Angle D

Since  ∠B = 18°

So

∠D = 18°

And If intersecting point of line BD and AC is O then

In the triangle Δ AOD

∠O = 90°

∠A = x

And we know that

Sum all angles of triangle = 180°

So

∠A + ∠O + ∠D = 180°

Putting values we get

x + 18° + 90° = 180°

x = 180 - 90 - 18 = 90 - 18 = 72°

Thus

x = 72°

Similarly

In triangle ΔBDC

∠B = ∠D

And

∠B = y

So

∠D = y

And

∠C = 29°

And

In triangle ΔDOC

∠O = 90°

We know that

Sum of all angles = 180°

∠D + ∠O + ∠C = 180°

Putting the values we get

y + 90° + 29° = 180°

y = 180 - 90 -29 = 90 - 29 = 61°

Thus

y = 61°  

Answer 2

Answer:

Angle x = 72°

Angle y = 61°

Step-by-step explanation:

In triangle ABD, AB = AD ( It means that triangle ABD is an isosceles triangle)

Therefore, angle B = angle D = 18°

In triangle AOD, angle A = x

angle O = 90°( diagonals bisect each other at 90°)

angle D = 18° ( base angle property of an isosceles triangle)

x + 90° + 18° = 180° ( Angle sum property of triangle)

x + 108° = 180°

x = 180° - 108°

x = 72°

Similarly, In triangle BDC, BC = DC

Therefore this triangle is an isosceles triangle

Therefore angle B = angle D = y

In triangle DOC,

angle D = y

angle O = 90°

angle C = 29°

y + 29° + 90° = 180° ( Angle sum property of triangle)

y + 119° = 180°

y = 180° - 119°

y = 61°

HOPE IT'S CLEAR TO YOU AND HELPS YOU