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# In triangle ABC, find z if AB = 5 and y = 40.

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Math Expert
Joined: 02 Sep 2009
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In triangle ABC, find z if AB = 5 and y = 40.  [#permalink]

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24 Oct 2017, 22:50
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Difficulty:

35% (medium)

Question Stats:

70% (01:09) correct 30% (01:11) wrong based on 82 sessions

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In triangle ABC, find z if AB = 5 and y = 40.

(1) BC = 5
(2) The bisector of angle B is perpendicular to AC.

Attachment:

2017-10-25_1048.png [ 5.96 KiB | Viewed 889 times ]

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In triangle ABC, find z if AB = 5 and y = 40.  [#permalink]

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24 Oct 2017, 22:54
Option D

From st1 we can conclude that this is an isosceles triangle. Hence x=40. Hence z=100. Hence sufficient
From st2 we can draw a perpendicular line from B. From this new triangle we can find that half angle of z=50. Hence z=100. Hence sufficient

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In triangle ABC, find z if AB = 5 and y = 40.  [#permalink]

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31 Oct 2017, 10:49
Bunuel wrote:

In triangle ABC, find z if AB = 5 and y = 40.

(1) BC = 5
(2) The bisector of angle B is perpendicular to AC.

Attachment:
2017-10-25_1048.png

I went with D, both are sufficient.

St 1, gives us an isosceles triangle. Therefore, angle x and y both = 40, therefore z = 100.
St 2, if a bisector of an angle is perpendicular than it's isosceles, so angles x and y both equal 40.

Also, it appears I got this right, but the wrong way.
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In triangle ABC, find z if AB = 5 and y = 40. &nbs [#permalink] 31 Oct 2017, 10:49
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