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In the figure shown, what is the value of x ? : Problem Solving (PS)
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# In the figure shown, what is the value of x ?

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

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...

Next, let's focus on the BLUE triangle.

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.

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.

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°

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

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

A. 60

B. 80

C. 85

D. 90

E. 95

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.

Attachment:
PS00534_f006.jpg
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Re: In the figure shown, what is the value of x ? [#permalink]
I think x looks like 90 degree just by looking, am I right?
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Re: In the figure shown, what is the value of x ? [#permalink]
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ams3212 wrote:
I think x looks like 90 degree just by looking, am I right?

Good observation. Unfortunately, you cannot base an answer in GMAT Geometry questions just by visuals alone.
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Re: In the figure shown, what is the value of x ? [#permalink]
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Video solution from Quant Reasoning:
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Re: In the figure shown, what is the value of x ? [#permalink]
1
Kudos
Bunuel wrote:

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

A. 60

B. 80

C. 85

D. 90

E. 95

Attachment:
PS00534_f006.jpg

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