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In the figure shown, what is the value of x ?

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In the figure shown, what is the value of x ?  [#permalink]

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New post 25 Jun 2018, 04:19
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In the figure shown, what is the value of x ?


A. 60

B. 80

C. 85

D. 90

E. 95



NEW question from GMAT® Official Guide 2019


(PS00534)


Attachment:
PS00534_f006.jpg
PS00534_f006.jpg [ 33.29 KiB | Viewed 3094 times ]

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Re: In the figure shown, what is the value of x ?  [#permalink]

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New post 25 Jun 2018, 06:44
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Bunuel wrote:
Image

In the figure shown, what is the value of x ?


A. 60

B. 80

C. 85

D. 90

E. 95



NEW question from GMAT® Official Guide 2019


(PS00534)


Attachment:
The attachment PS00534_f006.jpg is no longer available


See the attached figure..
Since exterior angles are 150, interior angles will be 180-150=30..
Therefore the third angle in the above triangle=180-30-30=120..
So adjoining angle =180-120=60..
In the below triangle X+60+30=180..
x=90

D
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Re: In the figure shown, what is the value of x ?  [#permalink]

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New post 25 Jun 2018, 04:34
1

Solution



To find:
    • The value of the angle x, in the given figure

Approach and Working:
We name the points of the diagram as follows, for our convenience of solving:

Image

    • Now, angle ACD = 180 – 150 = 30
    • Similarly, angle CAB = 180 – 150 = 30

If we consider triangle ABC, CBE is an external angle
    • Hence, angle CBE = ACD + CAB = 30 + 30 = 60

Now, considering triangle BDE,
    • Angle DBE = angle CBE = 60
    • Angle DEB = 180 – 150 = 30
    • Therefore, angle BDE = x = 180 – (60 + 30) = 180 – 90 = 90

Hence, the correct answer is option D.

Answer: D
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Re: In the figure shown, what is the value of x ?  [#permalink]

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New post 25 Jun 2018, 07:04
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Top Contributor
Bunuel wrote:
Image

In the figure shown, what is the value of x ?


A. 60

B. 80

C. 85

D. 90

E. 95
Attachment:
PS00534_f006.jpg


Since angles on a line must add to 180°, we can see that there are three 30° angles in our diagram...
Image

Next, let's focus on the BLUE triangle.
Image
Since angles in a triangle must add to 180° (and since we already have two angles measuring 30° each), the third angle must be 120°

Next, we have two angles sharing the same GREEN line.
Image
Since angles on a line must add to 180°, we can see that the other angle must be 60°

Finally, we can focus on the RED triangle.
Image
Since angles in a triangle must add to 180° (and since we already have two angles measuring 30° and 60°), the third angle (x) must be 90°

Answer: D

Cheers,
Brent
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Re: In the figure shown, what is the value of x ?  [#permalink]

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New post 26 Jun 2018, 17:09
Bunuel wrote:
Image

In the figure shown, what is the value of x ?


A. 60

B. 80

C. 85

D. 90

E. 95

Image

We can label some of the angles by variables as shown above. Recall that the measure of an exterior angle of a triangle is the sum of the two remote interior angles. So we have:

150 = b + c

150 = a + b

150 = x + y

and

y = a + c

Add up these four equations, we have:

450 + y = 2a + 2b + 2c + y + x

450 = 2(a + b + c) + x

Notice that a + b + c = 180 since they are the interior angles of a triangle. So we have:

450 = 2(180) + x

450 = 360 + x

90 = x

Alternate Solution:
Referring to the figure above, since a and 150 are supplementary, a = 30. Similarly, since c and 150 are supplementary, c = 30. The third angle in the triangle with angles x and y is also 30 for the same reasons. Since the measure of an exterior angle of a triangle is the sum of the two remote interior angles, y = a + c = 60. Now, we have a triangle where the interior angles are x, y = 60 and 30; thus x + 60 + 30 = 180, which implies x = 90.

Answer: D


Attachment:
PS00534_f006.jpg

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Re: In the figure shown, what is the value of x ? &nbs [#permalink] 26 Jun 2018, 17:09
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