Question

find X and Y in the following figure..
please answer fast
show all statements step by step​

Answer 1

Answer:

Here, ABCD is a rectangle.

As we know in rectangle both the diagonals are equal.

⇒ AC=BD

Also diagonals bisect each other.

⇒ AO=BO

⇒ ∠OAB=∠ABO [ Base angles of an equal sides are also equal ]

⇒ ∠ABO=y [ Given ]

∴ ∠OAB=y

we know that ∠DOC=100=∠AOB

and in △PQO,

∠ABO+∠OAB+∠AOB=180

=>y+y+100=180

=>2y=80

=>y=40

Since, ABCD is a rectangle, AB∥DC and AC is a transversal.

⇒ ∠DBA=∠BDC [ Alternate angles ]

so ∠BDC=y=40

therefore

∠ADB+∠BDC=90 [ Angle of an rectangle ]

x+40=90

=>x=90-40=50