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In the figure, if line CE bisects ∠ACB, then x =

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V
Joined: 02 Sep 2009
Posts: 58459
In the figure, if line CE bisects ∠ACB, then x =  [#permalink]

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New post 15 Oct 2018, 07:57
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

93% (01:24) correct 7% (00:56) wrong based on 33 sessions

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D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1013
WE: Supply Chain Management (Energy and Utilities)
Re: In the figure, if line CE bisects ∠ACB, then x =  [#permalink]

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New post 15 Oct 2018, 08:19
Bunuel wrote:
Image
In the figure, if line CE bisects ∠ACB, then x =

(A) 45

(B) 50

(C) 55

(D) 65

(E) 70



Given, line CE bisects ∠ACB. Hence ∠ACE=∠ECB

In the right angled triangle EBC, ∠ECB=180-90-x=90-x=∠ACE

Now, BD is perpendicular to hypotenuse AC of right angled triangle ABC.
Therefore, the triangle ABC is divided into two parts, i.e., Triangle ADB and Triangle BDC.
Triangle ADB is similar to the Triangle BDC. Hence on the basis of similarity, corresponding angles are equal
Hence, ∠BAD=∠DBC=40
So, ∠DCB=90-x+90-x=180-(90+40)=180-130=50
Or, 180-2x=50
Or, 2x=130
Or, x=65

Ans. (D)
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Joined: 19 Oct 2013
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Re: In the figure, if line CE bisects ∠ACB, then x =  [#permalink]

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New post 15 Oct 2018, 09:02
Bunuel wrote:
Image
In the figure, if line CE bisects ∠ACB, then x =

(A) 45

(B) 50

(C) 55

(D) 65

(E) 70


Attachment:
triangle.jpg


40 + 90 + angle ACB = 180

Angle ACB = 50

since CE bisects angle ACB then we know that ACE = 25 and ECB = 25

Sum of angles in triangle ECB will be x + 25 + 90 = 180

x + 115 = 180

x = 65

Answer choice D
GMAT Club Bot
Re: In the figure, if line CE bisects ∠ACB, then x =   [#permalink] 15 Oct 2018, 09:02
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