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# In the figure, triangles ABC and ABD are right triangles. What is the

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
In the figure, triangles ABC and ABD are right triangles. What is the  [#permalink]

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09 Oct 2018, 20:42
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Difficulty:

15% (low)

Question Stats:

86% (01:17) correct 14% (01:22) wrong based on 47 sessions

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In the figure, triangles ABC and ABD are right triangles. What is the value of x ?

(A) 20
(B) 30
(C) 50
(D) 70
(E) 90

Attachment:

triangle (1).jpg [ 21.64 KiB | Viewed 626 times ]

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Re: In the figure, triangles ABC and ABD are right triangles. What is the  [#permalink]

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10 Oct 2018, 01:26
Bunuel wrote:

In the figure, triangles ABC and ABD are right triangles. What is the value of x ?

(A) 20
(B) 30
(C) 50
(D) 70
(E) 90

Attachment:
triangle (1).jpg

For ABC to be right angle, angle C must be 90º

i.e. Angle ABD also must be 90º for the given geometry to exist

i.e. $$x = 90-20 = 70º$$

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Re: In the figure, triangles ABC and ABD are right triangles. What is the  [#permalink]

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19 Oct 2018, 13:30
Top Contributor
Bunuel wrote:

In the figure, triangles ABC and ABD are right triangles. What is the value of x ?

(A) 20
(B) 30
(C) 50
(D) 70
(E) 90
Attachment:
triangle (1).jpg

Let's add variables for a few more angles:

GIVEN: ∆ABC is a right triangle.
So, either ∠w or ∠v is 90°
However, if ∠w = 90° then ∆ABC CANNOT be a right triangle.
Why not?
Well, if ∠w = 90°, then ∠ABD must be GREATER THAN 90°, and since the 3 angles in ∆ABC must add to 180°, the other two angles (∠BAC and ∠BDC) must be less than 90°

So, we can be certain that ∠w does NOT equal 90°, which means ∠v = 90°
If ∠v = 90° and we know that ∠BAC = 20°, then w = 70° (since all 3 angles add to 180°)

GIVEN: ∆ABD is a right triangle.
If ∠v = 90°, then ∠u = 90°, which means ∠x cannot also equal 90°
So, in order for ∆ABD to be a right triangle, ∠ABD must equal 90°
If ∠ABD = 90 and ∠BAD = 20°, then x = 70° (since all 3 angles add to 180°)

Cheers,
Brent
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Re: In the figure, triangles ABC and ABD are right triangles. What is the   [#permalink] 19 Oct 2018, 13:30
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