In the Figure Shown, What is the Value of x GMAT Problem Solving

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

1. 60
2. 80
3. 85
4. 90
5. 95

Answer:

Approach Solution (1):

Since the exterior angles are 150, interior angles will be 180 – 150 = 30

\(\angle{ABC}=\angle{BAC}=\angle{DEC}=180-150=30\)
Therefore the third angle, \(\angle{BCA}\) ,in the \(\bigtriangleup {ABC}=180-30-30=120\)

So adjoining angle, \(\angle{BCE}=180 -\angle{ABC} =180-120 = 60\)

Take \(CDE\):

Sum of all angles = 180
x + 60 + 30 = 180
x = 90

Correct Option: D

Approach Solution (2):

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

Next, let’s focus on the Blue triangle

Since, angles in a triangle must add to 180 degrees (and since we already have two anlges measuring 30 degrees each), the third angle must be 120 degrees
Next, we have two angles sharing the same Green line

Since angles on a line must add to 180 degrees, we can see that the other angle must be 60 degrees.
Finally, we can focus on the Red triangle

Since angles in a triangle must add to 180 degrees (and since we already have two angles measuring 30 degrees and 60 degrees), the third angle (x) must be 9 degrees.

Correct Option: D

“In the figure shown, what is the value of x?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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