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In the figure shown, AB || CD. x = ?

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Senior RC Moderator
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In the figure shown, AB || CD. x = ?  [#permalink]

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New post Updated on: 05 Nov 2018, 11:38
3
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

73% (01:26) correct 27% (01:23) wrong based on 58 sessions

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In the figure shown, AB || CD. x = ?

A. 40
B. 70
C. 100
D. 110
E. 140

Source: Experts Global
Difficulty Level: 600

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Originally posted by SajjadAhmad on 19 Oct 2018, 12:47.
Last edited by SajjadAhmad on 05 Nov 2018, 11:38, edited 1 time in total.
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Re: In the figure shown, AB || CD. x = ?  [#permalink]

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New post 19 Oct 2018, 13:46
1
Let the point on AB making 100 deg be P, the point on CD making 30 deg be Q and the point in the middle making angle (x+10) deg be R.

Extending the 30 deg angle line QR to cut AB at some point E.


In triangle PRE angle RPE is 180-100=80 deg.

And ang QEP is 30 deg.
Transversal between parallel lines.
Interior opposite angles property.

So now for triangle PRE, angle PRQ is an external angle whose sum should be equal to sum of interior opposite angles.
Therefore, x+10 = 30+80
x = 100.

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Re: In the figure shown, AB || CD. x = ?  [#permalink]

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New post 24 Oct 2018, 22:08
1
Hi,

It is a popular concept in parallel lines.

Given, AB and CD are parallel to each other.

Lets draw line parallel to these lines (as given in the figure attached below) passing through point O,

Using alternate interior angles,

x+10 = 80+30

x = 110 -10

x = 100.

So the answer is C.
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Re: In the figure shown, AB || CD. x = ?   [#permalink] 24 Oct 2018, 22:08
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