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555-605 (Medium)|   Geometry|      
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Bunuel
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In the right triangle ABC, BD is perpendicular to AC and E is a point 02 Sep 2018, 23:33
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78% (02:02) correct 22% (02:03) wrong based on 108 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°

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image051.jpg
image051.jpg [ 2.26 KiB | Viewed 3408 times ]
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A
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In the right triangle ABC, BD is perpendicular to AC and E is a point 03 Sep 2018, 00:55
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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°

Show Spoiler
Attachment:
image051.jpg
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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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In the right triangle ABC, BD is perpendicular to AC and E is a point 03 Sep 2018, 01:05
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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°

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

TIA

Thank you = Kudos
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In the right triangle ABC, BD is perpendicular to AC and E is a point 03 Sep 2018, 01:10
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sumit411
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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°

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

Hope this helps!!!
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In the right triangle ABC, BD is perpendicular to AC and E is a point 03 Sep 2018, 01:11
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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°

Show Spoiler
Attachment:
image051.jpg
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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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In the right triangle ABC, BD is perpendicular to AC and E is a point 03 Sep 2018, 01:23
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sumit411
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[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°

Show Spoiler
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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In the right triangle ABC, BD is perpendicular to AC and E is a point 03 Sep 2018, 02:09
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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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In the right triangle ABC, BD is perpendicular to AC and E is a point 24 Aug 2020, 21:59
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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°

Show Spoiler
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
Show more

How do you arrive at 40 + y = 90?
I've got how you come up with x, however, I do not see why 40 + y should sum up to 90 degree.

Could someone shed light in this, maybe with a graphic?

Thank you very very much! :please:
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