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# In right triangle ABC above, if CD is the bisector of angle ACB, then

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Math Expert
Joined: 02 Sep 2009
Posts: 55236
In right triangle ABC above, if CD is the bisector of angle ACB, then  [#permalink]

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24 Aug 2017, 23:53
00:00

Difficulty:

15% (low)

Question Stats:

92% (00:49) correct 8% (00:18) wrong based on 34 sessions

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In right triangle ABC above, if CD is the bisector of angle ACB, then x =

(A) 15
(B) 20
(C) 25
(D) 40
(E) 50

Attachment:

2017-08-25_1042_002.png [ 6.43 KiB | Viewed 2685 times ]

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In right triangle ABC above, if CD is the bisector of angle ACB, then  [#permalink]

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25 Aug 2017, 00:24

Since CD is the bisector of angle ACB, Angle DCB = 20 degree

The third angle in the triangle DCB is 180 - (20 + 90) = 70

Since the sum of angles in a straight line is 180, the angle CDA = 110
Now, x + 20 + 110 = 180(the sum of three angle is a triangle is 180)

Therefore, the value of x is 50(Option E)
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Re: In right triangle ABC above, if CD is the bisector of angle ACB, then  [#permalink]

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25 Aug 2017, 03:09
Taking triangle ABC as a whole we can see that

x + 2*20 + 90 = 180 ( Since CD is the bisector of angle C )

hence, x = 50

Option E is correct
Re: In right triangle ABC above, if CD is the bisector of angle ACB, then   [#permalink] 25 Aug 2017, 03:09
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