Difficult Geometry

[akhilsuhag]

OA C

[prateek_guy2004]

Hey akhil

This is a Gmat prep ques....Are you sure that the answer is C

[akhilsuhag]

Yeah the answer is C
I just checked!!

[jbivins]

If we knew the length of the angles on either side of x we could determine the value of x since all three angles would sum to 180. I'm having a hard time trying to figure out how to explain this....with out a picture. Say that both of the angles next to x can be represented by Z and Y

1. Z+X+Y=180 - straight line so the angles sum to 180

All the angels of the triangle sum to 180 as well and we know one of the angels is 90 since it's a right triangle. There for the sum of the largest triangles remaining angles is 90.
I will represent those angles as A and B.
2. A+B=90

With both pieces of information we now know that we have two isosceles triangles. on either side of x so know the properties of isosceles triangles we get the following equations
3. 2Z+A=180 z=(180-A)/2
4. 2Y+B=180 y=(180-B)/2

combining equations 3 4 and 1 we get

x+((180-A)/2)+((180-B)/2)=180

some basic algebra and we get

2x+360-(A+B)=360 from equation 2 we know A+B equals 90.

At this point we know we can solve for x so no point in going on
I believe the answer is c with 45 being the explicit answer

[GMATGuruNY]

I posted a solution here:

https://www.beatthegmat.com/ds-geometry- ... 70380.html

[prateek_guy2004]

Mitch Hunt excellent approach ...even i thought at first glance about 180 degree straight line but then after spending sometime on it i came to a conclusion that its E.

But yes great way to solve this...........