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

Question

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

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Sebastian Discussed

In the given figure,

A B ∥ C D

and

EF ∥ G H

. Find the values of

x, y, z

and

t

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

From the figure we know that

∠ PRQ = x^{o} = 60^{o}

as the vertically opposite angles are equal

We know that

EF ∥ G H

and

RQ

is a transversal

From the figure we also know that

∠ PRQ

and

∠ RQS

are alternate angles

so we get

∠ PRQ = ∠ RQS

∠ x = ∠ y = 60^{o}

We know that

A B ∥ C D

and

PR

is a tranversal from the figure we know that

∠ PR D

and

∠ A PR

are alternate angles

So we get

∠ PR D = ∠ A PR

it can be written as

∠ PRQ + ∠ QR D = ∠ A PR

by substituting the values we get

x + ∠ QR D = 110^{o}

60^{o} + ∠ QR D = 110^{o}

∠ QR D = 50^{o}

according to the

△ QRS

we can write

∠ QR D + ∠ QSR + ∠ RQS = 180^{o}

by substituting the values

∠ QR D + t^{o} + y^{o} = 180^{o}

50^{o} + t^{o} + 60^{o} = 180^{o}

t^{o} = 70^{o}

we know that

A B ∥ C D

and

G H

is a transversal from the figure we know that

z^{o}

and

t^{o}

are alternate angles

so we get

z^{o} = t^{o} = 70^{o}

therefore the values of

x, y, z, t

are

60^{o}, 60^{o}, 70^{o}, 70^{o}

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Question Text	In the given figure, $A B ∥ C D$ and $EF ∥ G H$ . Find the values of $x, y, z$ and $t$
Answer Type	Text solution:1
Upvotes	151

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

Text solutionVerified

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