Question

If ABCD is a rectangle then find value of ‘x’ and ‘y’.​

Answer 1

Answer:

∠ABC = 90

∠DBC = 90 / 2

          = 45

x = 45

y = ?

  = ∠D + ∠C - 180 ( 180 because the angle sum propery of triangle )

  = 45 + 45 - 180

  = 90 - 180

  = 90

Y = 90

X= 45; Y = 90

Answer 2

☆ To find :

The values of x and y in the rectangle given.

☆ Solution :

Here ,we can observe that the Diagonals are equal because they bisect each other at O.

Hence,

AC = BD , AO = OB

∴ We can say that ∆AOB is an isosceles triangle.

∠OAB = ∠OBA = 35°

Thus,

• Value of x :

→ x° + ∠OBA = 90°

→ x° + 35° = 90°

→ x° = 90° - 35°

→ x° = 55°

Therefore,

• The value of x° is 55°.

Now, finding the value of y.

In ∆ AOB

• ∠OAB = 35°

• ∠AOB = ?

• ∠ABO = 35°

Thus,

↦ ∠OAB + ∠AOB + ∠OBA = 180° [Angle sum property of ∆]

↦ 35° + ∠AOB + 35° = 180°

↦ 70° + ∠AOB = 180°

↦ ∠AOB = 180° - 70°

↦ ∠AOB = 110°

Therefore,

If ∠AOB = 110° then ∠DOC = 110°

[Because vertically opposite angles are equal].

Thus,

• The value of y(∠DOC) is 110°.