# in the given figure abcd is a rectangle find the value of x and y

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## In Fig. 1, ABCD is a rectangle. Find the values of x and y .

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## In Fig. 1,ABCD is a rectangle. Find the values of x and y.

∵ ABCD is a rectangle, the length of opposites sides are equal.Easy Open in App Solution Verified by Toppr ⇒AB=CDandAD=BC x+y=30 ...... (1) x−y=14 ..... (2)

Adding (1)+(2)⇒2x=44⇒x=

2 44 =22 cm.

Subtracting (1)−(2)⇒2y=16⇒y=

2 16 =8 cm. ∴x=22 cmandy=8 cm.

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## In fig. 1, ABCD is a rectangle. Find the values of x and y.

In fig. 1, ABCD is a rectangle. Find the values of x and y.

Byju's Answer Standard X Mathematics

Multiplying/Dividing a Negative Entity

In fig. 1, AB... Question

In fig. 1, ABCD is a rectangle. Find the values of x and y.

Open in App Solution

Given, ABCD is a rectangle.

∴ AB = CD ⇒ 30 = x + y

or x + y = 30 ..... (i)

Similarly, AD = BC ⇒ 14 = x - y

or x - y = 14 .......(ii)

On adding eq. (i) and (ii), we get

2x = 44 ⇒ x = 22

Putting the value of x in eq. (i), we get

22 + y = 30 ⇒ y = 30 -22 ⇒ y = 8 So, x = 22, y = 8. Suggest Corrections 62

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Free solutions for R S Aggarwal Solutions - Mathematics - Class 9 Chapter 11 - Quadrilaterals Quadrilaterals Exercise 10B question 13. These explanations are written by Lido teacher so that you easily understand even the most difficult concepts

## RS Aggarwal Solutions Class 9 Mathematics Solutions for Quadrilaterals Exercise 10B in Chapter 10 - Quadrilaterals

Prev Question 13 Next

In each of the figures given below, ABCD is a rectangle. Find the values of x and y in each case.

(i)

Answer:

(i) 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 = 35

By using the sum property of triangle

∠ AOB + ∠ OAB + ∠ OBA = 180

By substituting the values we get

∠ AOB + 35+ 35 = 180

On further calculation

∠ AOB = 180 - 35 - 35

By subtraction ∠ AOB = 180 - 70 ∠ AOB = 110

From the figure we know that the vertically opposite angles are equal

∠ DOC = ∠ AOB = y = 110

In △ ABC

We know that ∠ ABC = 90

Consider △ OBC We know that

∠ OBC = x = ∠ ABC - ∠ OBA

By substituting the values

∠ OBC = 90 - 35 By subtraction ∠ OBC = 55

Therefore, x = 55 and y = 110.

(ii) From the figure we know that the diagonals of a rectangle are equal and bisect each other.

Consider △ AOB We get OA = OB

We know that the base angles are equal

∠ OAB = ∠ OBA

By using the sum property of triangle

∠ AOB + ∠ OAB + ∠ OBA = 180

By substituting the values

110 + ∠ OAB + ∠ OBA = 180

We know that ∠ OAB = ∠ OBA

So we get 2 ∠ OAB = 180 - 110 By subtraction 2 ∠ OAB = 70 By division ∠ OAB = 35

We know that AB || CD and AC is a transversal

From the figure we know that ∠ DCA and ∠ CAB are alternate angles

∠ DCA = ∠ CAB = y = 35

Consider △ ABC We know that ∠ ACB + ∠ CAB = 90 So we get ∠ ACB = 90 - ∠ CAB

By substituting the values in above equation

∠ ACB = 90 - 35 By subtraction ∠ ACB = x = 55

Therefore, x = 55 and y = 35.

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