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08 Aug 2017, 10:34
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D
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Difficulty:
15%
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Question Stats:
80% (00:42) correct
20%
(00:46)
wrong
based on 51
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Not Attempted Yet
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 2506 times ]
08 Aug 2017, 11:16
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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)
08 Aug 2017, 18:41
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Bunuel
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
Answer D
