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# In the ﬁgure shown, lines k and m are parallel to each other. Is x = z

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Re: In the ﬁgure shown, lines k and m are parallel to each other. Is x = z [#permalink]
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WillGetIt

In the ﬁgure shown, lines k and m are parallel to each other. Is x = z ?

(1) x = w
(2) y = 180 - w

Attachment:
Untitled.png

Given : Figure in which k || m
DS : x = z ?
From figure, y = 180 -x

Option 1 : x = w
SO sum of all angles of a quadrilateral = 360
-> y + w +(180 -z) + x(alternate angle) = 360
-> 180 -x + x + 180 - z + x = 360
-> x = z
SUFFICIENT

Option 2 : Y = 180 - w = 180 - x
-> x = w which is smae as option 1
SUFFICIENT

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Re: In the ﬁgure shown, lines k and m are parallel to each other. Is x = z [#permalink]
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WillGetIt
In the ﬁgure shown, lines k and m are parallel to each other. Is x = z ?

(1) X=W
(2) y = 180 —w

1) statement one tells us that X=W..
but W=Z since both are alternate angles between two llel lines.. suff

2) y=180-w... also y=180-x as y and x are supplementary angles.. so w=x , same info as statement 1... suff
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Re: In the ﬁgure shown, lines k and m are parallel to each other. Is x = z [#permalink]
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I made a mistake by discarding second statement since it did not provide any new information. Duh.
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Re: In the ﬁgure shown, lines k and m are parallel to each other. Is x = z [#permalink]
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WillGetIt

In the ﬁgure shown, lines k and m are parallel to each other. Is x = z ?

(1) x = w
(2) y = 180 - w

Attachment:
Untitled.png
Solution:

Question Stem Analysis:

We need to determine whether x = z. We see that x + y = 180. Furthermore, we are given that lines k and m are parallel, so w = z because they are alternate interior angles.

Statement One Alone:

Since x = w and w = z, then x = z. Statement one alone is sufficient.

Statement Two Alone:

Since y = 180 - w and w = z, then y = 180 - z or z + y = 180. Since x + y = 180 and z + y = 180, we see that x = z. Statement two alone is sufficient.

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Re: In the ﬁgure shown, lines k and m are parallel to each other. Is x = z [#permalink]
Guys can you tell me where can learn the angles stuff?
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Re: In the ﬁgure shown, lines k and m are parallel to each other. Is x = z [#permalink]
The Diagram really confused me, whether "W" was alternate angle of X or Z.
How do I determine this in exams, in such cases ? do i have to see the degree symbol, which was on right side
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Re: In the ﬁgure shown, lines k and m are parallel to each other. Is x = z [#permalink]
alternate angles.

Just derive algebraically that x= w in either statement to determine that each is sufficient.
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Re: In the ﬁgure shown, lines k and m are parallel to each other. Is x = z [#permalink]
(1) x = w

From the figure we can conclude w = z, as we're told lines k and m are parallel to each other (alternate angles are equal). From statement 1 we're told x = w. Thus x = w = z. SUFFICIENT.

(2) y = 180 - w

This statement tells us x = w. Since w = z, z = x. SUFFICIENT.

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Re: In the ﬁgure shown, lines k and m are parallel to each other. Is x = z [#permalink]
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WillGetIt

In the ﬁgure shown, lines k and m are parallel to each other. Is x = z ?

(1) x = w
(2) y = 180 - w

Attachment:
Untitled.png

(1) As the figure is a parallelogram; $$w=z$$; as they are alternate angels, Given $$x=w, \ so \ x=z$$; Sufficient.

(2) As $$y=180-w$$, $$x=180-180+w=w$$, now for the condition described in option 1 $$x=z$$; Sufficient.

The answer is $$D$$
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Re: In the ﬁgure shown, lines k and m are parallel to each other. Is x = z [#permalink]
St1 - x = w
w = z (alternating angles)

Sufficient.

St2 - y = 180 - w

180 - w = 180 - x (by rule of supplementary angles)

x = w

Sufficient.

D.
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In the ﬁgure shown, lines k and m are parallel to each other. Is x = z [#permalink]
WillGetIt

In the ﬁgure shown, lines k and m are parallel to each other. Is x = z ?

(1) x = w
(2) y = 180 - w

Attachment:
Untitled.png

When a line transverses two parallel line we end up with a couple of special properties. One of which is that the corresponding acute and obtuse angles are equal to each other. So from analyzing the picture in the stem we can conclude right off the bat that W=Z.

Statement 1:
If X = W, then X = W = Z, so X must be equal to Z

Statement 2:
Given that the angles X and Y are supplementary, we can conclude that X+Y = 180, and furthermore with the information provided in statement two we can say that X + 180 - W = 180, so X = W. Since in the stem we concluded that W=Z then we can now conclude that X = W = Z, so it must be the case that X = Z.
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Re: In the gure shown, lines k and m are parallel to each other. Is x = z [#permalink]
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Re: In the gure shown, lines k and m are parallel to each other. Is x = z [#permalink]
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