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In the figure, ABCD is a rhombus. Find the value of x and y.

Question

In the figure, $A BC D$ is a rhombus. Find the value of $x$ and $y$ .

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In the figure,

A BC D

is a rhombus. Find the value of

x

and

y

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

We know that all the sides are equal in a rhombus

Consider

△ A B D

We get

A B = A D

and

∠ A B D = ∠ A D B

It can be written as

x = y .... (1)

Consider

△ A BC

We get

A B = BC

and

∠ C A B = ∠ A CB

We know that

∠ A CB = 40^{o}

by using the sum property of a triangle

∠ B + ∠ C A B + ∠ A CB = 180^{o}

By substituting the values in equation

∠ B = 40^{o} + 40^{o} = 180^{o}

∠ B = 180^{o} - 80^{o}

∠ B = 100^{o}

∠ D BC

can be written as

∠ D BC = ∠ B - x^{o}

by sbstituting the values

∠ D BC = 100^{o} - x^{o}

From the figure we know that

∠ D BC

and

∠ A D B

are alternate angles

∠ D BC = ∠ A D B = y^{o}

by subsituting the value of

∠ D BC

100^{o} - y^{o} = y^{o}

consider the equation (1) we know that

x = y

100^{o} - x^{o} = x^{o}

2 x^{o} = 100^{o}

x^{o} = 50^{o}

therefore

x = y = 50^{o}

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Question Text	In the figure, $A BC D$ is a rhombus. Find the value of $x$ and $y$ .
Answer Type	Text solution:1
Upvotes	150

In the figure, ABCD is a rhombus. Find the value of x and y.

Text solutionVerified

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In the figure, $A BC D$ is a rhombus. Find the value of $x$ and $y$ .