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

Good question and quite a learning...

Out of curiousity, can this sum be solved in less than 2mins that too under "GMAT exam" conditions that too at first sight??

Could you please elaborate on the highlighted one . As to , how did you arrive at Angle EBD = Angle ECD ??

Thanks,
Jyothi

this is my approach.
we can rewrite the sum of the big triangles as:
180=x+2z
where z = 180-2x.

based on statement 1, we can solve for x.
statement 2 doesn't tell us much.

Detailed Solution

Step-I: Given Info

The question asks us to find the value of x as indicated in the figure, using the 2 statements given.

Step-II: Interpreting the Question Statement

To find the value of x from the given figure, we have to make use of different concepts of geometry based on the information given in the individual statements.
We will also modify the figure as per our convenience to be able to solve the problems easily.
The modified figure is attached as Pic.png(Attached), with all angles marked.

Step-III: Statement-I

Statement- I gives us the information that AD = AE = BE = CD = BC.

Now from the Pic.png(Attached) and using the information in statement 1, we know

Equation 1: x=t=z (Because AE=BE=AD) (Concept Used: Angles opposite to equal sides are equal)
Equation 2: v=t+s & w=z+y (Because BE=BC=CD) (Concept Used: Angles opposite to equal sides are equal)
Equation 3: w=x+t (Concept Used: Exterior angle of a traingle is equal to the Sum of Interior opposite angles)

Combining the results of the above 3 equations

By equation 2 and 3;

w=z+y=x+t.
From Equation 1 x=z=t, so we have x+y=2*x
This means y=x
Also combining this result with equation 1&2, we get y=x=z=t=s

Now considering Triangle ABC,
We know that Sum of Angles in a triangle is 180 degree,

So, \(x+z+y+t+s = 180\)

Since all these 5 angles are equal to each other, we have 5*x=180 or x=36

Hence, statement 1 is sufficient to answer the question.

Step-IV: Statement-II

Statement- II gives us information that x=y. We dis drive this result from statement 1, but it is not sufficient to answer the question since neither value of x or y is given nor any other condition of the triangle is given to come to a definite value of x.

Hence, statement 2 is not sufficient to answer this question.

Step-V: Combining Statements I & II

Since, we have a unique answer from Statement- I so, we don’t need to combine Statements- I & II.
Hence, the correct answer is Option A

Key Takeaways

1. Use of Property: Exterior angle of a triangle is equal to the sum of the interior opposite angles.
2. Use of Property: Angles opposite to equal sides are equal.

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