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In the given figure, AB CD. Find the values of x,y and z.

Question

In the given figure, $A B ∥ C D$ . Find the values of $x, y$ and $z$ .

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Daniel Discussed

In the given figure,

A B ∥ C D

. Find the values of

x, y

and

z

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

It is given that

A B ∥ C D

and

EF

is a transversal

from the fiture we know that

∠ A EF

and

∠ EFG

are alternate angles

so we get

∠ A EF = ∠ EFG = 75^{o}

∠ EFG = y = 75^{o}

from the figure we know that

∠ EFC

and

∠ EFG

form a linear pair of angles

so we get

∠ EFC + ∠ EFG = 180^{o}

it can also be written as

x + y = 180^{o}

by substituting the value of

y

we get

x + 75^{o} = 180^{o}

x = 105^{o}

from the figure based on the exterior angle property it can be written as

∠ EG D = ∠ EFG + ∠ FEG

by substituting the values in the above equation we get

125^{o} = y + z

125^{o} = 75^{o} + z

z = 50^{o}

therefore the values of

x, y, z

are

105^{o}, 75^{o}, 50^{o}

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Question Text	In the given figure, $A B ∥ C D$ . Find the values of $x, y$ and $z$ .
Answer Type	Text solution:1
Upvotes	150

In the given figure, AB∥CD. Find the values of x,y and z.

Text solutionVerified

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In the given figure, $A B ∥ C D$ . Find the values of $x, y$ and $z$ .