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In the figure above, x =

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Joined: 02 Sep 2009
Posts: 54440
In the figure above, x =  [#permalink]

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08 Aug 2017, 10:34
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Difficulty:

35% (medium)

Question Stats:

72% (00:35) correct 28% (00:56) wrong based on 27 sessions

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In the figure above, x =

(A) 35
(B) 55
(C) 125
(D) 145
(E) 150

Attachment:

2017-08-08_2133.png [ 10.02 KiB | Viewed 611 times ]

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Re: In the figure above, x =  [#permalink]

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08 Aug 2017, 11:16

In the right angled triangle with 35 degree angle, the third angle is 180 - 90 - 35 = 65

For two intersecting triangles, the angle opposite is 65 degree and the third angle is again 35 degree,
because the triangle is right angled.

Since the sum of angles in a straight line is 180, x + 35 = 180 => x = 180 - 35 = 145(Option D)
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In the figure above, x =  [#permalink]

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08 Aug 2017, 18:41
Bunuel wrote:

In the figure above, x =

(A) 35
(B) 55
(C) 125
(D) 145
(E) 150

Attachment:
2017-08-08_2133.png

If any two angles of any two triangles are congruent, the third angle is congruent, and the triangles are similar.

(The AA postulate comes from the fact that interior angles of a triangle always sum to 180. Two of three angles equal means both third angles are equal, too.)

Both triangles have a 90° angle, and congruent vertical angles. The unlabeled third angle of the triangle on the left therefore is 35°. Angle x is on the same straight line as that third angle, so x + 35 = 180.

x = 145

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In the figure above, x =   [#permalink] 08 Aug 2017, 18:41
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