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

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

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New post 02 Sep 2018, 22:33
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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
image051.jpg [ 2.26 KiB | Viewed 601 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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New post 02 Sep 2018, 23:55
Bunuel wrote:
Image
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

Answer: option A
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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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New post 03 Sep 2018, 00:05
GMATinsight wrote:
Bunuel wrote:
Image
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

Answer: option A
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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New post 03 Sep 2018, 00:10
sumit411 wrote:
GMATinsight wrote:
Bunuel wrote:
Image
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

Answer: option A
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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New post 03 Sep 2018, 00:11
Bunuel wrote:
Image
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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Re: In the right triangle ABC, BD is perpendicular to AC and E is a point  [#permalink]

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New post 03 Sep 2018, 00:23
GMATinsight wrote:
sumit411 wrote:
GMATinsight wrote:
[quote="Bunuel"]Image
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

Answer: option A
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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New post 03 Sep 2018, 01:09
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
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Re: In the right triangle ABC, BD is perpendicular to AC and E is a point &nbs [#permalink] 03 Sep 2018, 01:09
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In the right triangle ABC, BD is perpendicular to AC and E is a point

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