Question

In the adjoining figure ABCD is a rectangle find values of x & y​

Answer 1

Answer:

value of x=55° and y =90°

Answer 2

Answer:

x=55o, y=110o

Step-by-step explanation:

In the figures, ABCD is a rectangle. Find the values of x and y.

from the figure we know that the diagonals are equal and bisect at point O

Consider △AOB

we get

AO=OB

We know that the base angles are equal

∠OAB=∠OBA=35o

By using the sum property of the triangle

∠AOB+∠OAB+∠OBA=180o

By substituting the values  we get

∠AOB+35o+35o=180o

∠AOB=180o−70o

∠AOB=110o

from the figure, we know that the vertically opposite angles are equal

⇒∠DOC=∠AOB=y=110o

In △ABC

We know that ∠ABC=90o

Consider △OBC

We know that

∠OBC=xo=∠ABC−∠OBA

By substituting the values

∠OBC=90o−35o

∠OBC=55

therefore x=55o, y=110o