karthikpandian19 wrote:



(A) 60

(B) 75

(C) 90

(D) 105

(E) 120

Consider triangle BFE

BF = 1/2 BE & angle (BFE) = 90
=> the triangle is a 30-60-90 triangle , with angle(BEF) = 30 and angle(FBE) = 60

As the lines AF and BE are parallel , angle(AFB) = angle(FBE) = 60 ( alternate interior angles)

Since AB = BF, triangle ABF is isosceles triangle.
therefore angle(BAF) = angle(AFB) = 60 and angle(ABF) = 60 (180 - 120)(sum of angles of a triangle)

angle(ABE) = angle (ABF) + angle(FBE)
angle(ABE) = 60 + 60 =120

Finally ,
BE & CD are parallel , so angle(ABE) = angle(ACD) = 120 (corresponding angles)

Hence x= 120
the correct ans is E

Hi,

I didn't understand this part.

"BF = 1/2 BE & angle (BFE) = 90
=> the triangle is a 30-60-90 triangle , with angle(BEF) = 30 and angle(FBE) = 60 "

I understand sum of angles of Triangle is 180, but didn't get this one.

Also, I wanted to ask which are the Fundamentals to remember while solving problems related to Triangles?

Please help.

namratasingh wrote:Hi,

I didn't understand this part.

"BF = 1/2 BE & angle (BFE) = 90
=> the triangle is a 30-60-90 triangle , with angle(BEF) = 30 and angle(FBE) = 60 "

I understand sum of angles of Triangle is 180, but didn't get this one.

Also, I wanted to ask which are the Fundamentals to remember while solving problems related to Triangles?

Please help.

Hi namratasingh:

There are two special right angled triangles that the GMAT expects you to know.

First is the 30-60-90 triangle. In the 30-60-90 triangle, the sides opposites to the angles are in the ratio 1:sqrt(3):2. Any time you see a right angled triangle with two sides in 1:2, 1:sqrt(3), or 2:sqrt(3) ratio, you need to recognize if the triangle is 30-60-90.

The other special triangle is 45-45-60. In this one, the sides are in the ratio 1:1:sqrt(2). So anytime you see a right angled triangle in which sides are in the ratio 1:sqrt(2), you need to determine whether the triangle is 45-45-90.

Besides these two, there are some other right angled triangles, in which the computation is made easier if the sides are in a particular ratio.

a. 3:4:5 right angled triangle. (This may show up as 6:8:10 or 15:20:25 right angled triangle etc.)
b. 5:12:13 right angled triangle.(This may also show up as 10:24:26 right angled triangle etc.)

This is the bulk of it. Remembering this will help you immensely in triangle geometry questions.

Let me know if this helps

karthikpandian19 wrote:



(A) 60

(B) 75

(C) 90

(D) 105

(E) 120

Extend the lines so that it's easier to see which angles are equal.



Let AB=1, BF=1, and BE=2, satisfying the relationships given in the question stem.
A right triangle with a hypotenuse twice the length of a leg is a 30-60-90 triangle.
The sides of a 30-60-90 triangle are in a ratio of 1:√3:2.
The smallest angle is opposite the shortest side.
Thus, ∠BEF = 30.
Follow the colored angles.

Blue angles:
Since line AF is parallel to line BE, ∠AFG = ∠BEF = 30.

Green angles:
Since ∠AFG = 30 and ∠BFE = 90, ∠AFB = 60.
Since AB = BF, ∠BAF = ∠AFB = 60.

Red angles:
Since ∠BAF = 60, ∠GAF = 120.
Since line CD is parallel to line AF, x = ∠GAF = 120.

The correct answer is E.

OA is E

karthikpandian19 wrote:



(A) 60

(B) 75

(C) 90

(D) 105

(E) 120