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# In the right triangle ABC, BD is perpendicular to AC and E is a point

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
In the right triangle ABC, BD is perpendicular to AC and E is a point  [#permalink]

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02 Sep 2018, 23:33
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Difficulty:

35% (medium)

Question Stats:

75% (02:01) correct 25% (02:29) wrong based on 37 sessions

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In the right triangle ABC, BD is perpendicular to AC and E is a point on AC such that the angle ABE is 30° and the angle EBD is 20°. What is y - x = ?

A. 10°
B. 20°
C. 30°
D. 50°
E. 90°

Attachment:

image051.jpg [ 2.26 KiB | Viewed 904 times ]

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Re: In the right triangle ABC, BD is perpendicular to AC and E is a point  [#permalink]

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03 Sep 2018, 00:55
Bunuel wrote:

In the right triangle ABC, BD is perpendicular to AC and E is a point on AC such that the angle ABE is 30° and the angle EBD is 20°. What is y - x = ?

A. 10°
B. 20°
C. 30°
D. 50°
E. 90°

Attachment:
image051.jpg

Angle BED = x+30 (Exterior angle is sum of other two interior angles of triangle ABE) = (180-90-20) = 70

i.e. x = 70-30 = 40

Angle BDE = 40+y = 90 (Given)

i.e. y = 50

i.e. y - x = 50 - 40 = 10º

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Joined: 07 Oct 2017
Posts: 252
Re: In the right triangle ABC, BD is perpendicular to AC and E is a point  [#permalink]

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03 Sep 2018, 01:05
GMATinsight wrote:
Bunuel wrote:

In the right triangle ABC, BD is perpendicular to AC and E is a point on AC such that the angle ABE is 30° and the angle EBD is 20°. What is y - x = ?

A. 10°
B. 20°
C. 30°
D. 50°
E. 90°

Attachment:
image051.jpg

Angle BED = x+30 (Exterior angle is sum of other two interior angles of triangle ABE) = (180-90-20) = 70

i.e. x = 70-30 = 40

Angle BDE = 40+y = 90 (Given)

i.e. y = 50

i.e. y - x = 50 - 40 = 10º

Can you please explain how you got x+30=70

TIA

Thank you = Kudos
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Re: In the right triangle ABC, BD is perpendicular to AC and E is a point  [#permalink]

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03 Sep 2018, 01:10
sumit411 wrote:
GMATinsight wrote:
Bunuel wrote:

In the right triangle ABC, BD is perpendicular to AC and E is a point on AC such that the angle ABE is 30° and the angle EBD is 20°. What is y - x = ?

A. 10°
B. 20°
C. 30°
D. 50°
E. 90°

Attachment:
image051.jpg

Angle BED = x+30 (Exterior angle is sum of other two interior angles of triangle ABE) = (180-90-20) = 70

i.e. x = 70-30 = 40

Angle BDE = 40+y = 90 (Given)

i.e. y = 50

i.e. y - x = 50 - 40 = 10º

Can you please explain how you got x+30=70

TIA

Thank you = Kudos

Angle BED in triangle BED = 180 - Angle EBD - Angle BDE = 180 - 20 - 90 = 70

Hope this helps!!!
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Re: In the right triangle ABC, BD is perpendicular to AC and E is a point  [#permalink]

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03 Sep 2018, 01:11
Bunuel wrote:

In the right triangle ABC, BD is perpendicular to AC and E is a point on AC such that the angle ABE is 30° and the angle EBD is 20°. What is y - x = ?

A. 10°
B. 20°
C. 30°
D. 50°
E. 90°

Attachment:
image051.jpg

given
ABD=50
since BD is perpendicular , BDA=BDC=90
x= 180 - (90+50)=40

similarly,
ABC = 90
DBC = 90-50=40
y=180-(90+40) = 50

y-x=10
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Joined: 07 Oct 2017
Posts: 252
Re: In the right triangle ABC, BD is perpendicular to AC and E is a point  [#permalink]

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03 Sep 2018, 01:23
GMATinsight wrote:
sumit411 wrote:
GMATinsight wrote:
[quote="Bunuel"]
In the right triangle ABC, BD is perpendicular to AC and E is a point on AC such that the angle ABE is 30° and the angle EBD is 20°. What is y - x = ?

A. 10°
B. 20°
C. 30°
D. 50°
E. 90°

Attachment:
image051.jpg

Angle BED = x+30 (Exterior angle is sum of other two interior angles of triangle ABE) = (180-90-20) = 70

i.e. x = 70-30 = 40

Angle BDE = 40+y = 90 (Given)

i.e. y = 50

i.e. y - x = 50 - 40 = 10º

Can you please explain how you got x+30=70

TIA

Thank you = Kudos

Angle BED in triangle BED = 180 - Angle EBD - Angle BDE = 180 - 20 - 90 = 70

Hope this helps!!![/quote]Hey thanks a lot. I completely missed BD is perpendicular.

Thank you = Kudos
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Re: In the right triangle ABC, BD is perpendicular to AC and E is a point  [#permalink]

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03 Sep 2018, 02:09
If BD is PPDCL to AC then:
-Ang BDC= 90 therefore, X+(20+30)+90=180 => X=40
-Ang BDA= 90 therefore Y+90+(90-20-30)=180 => Y= 50

Y-X= 50-40=10
Re: In the right triangle ABC, BD is perpendicular to AC and E is a point   [#permalink] 03 Sep 2018, 02:09
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