In the parallelogram above, what is the value of y?

Question

6zxysp.png In the parallelogram above, what is the value of y? A) 10 B) 15 C) 20 D) 35 E) 45

GMATinsight · Accepted Answer

Hi  pacifist85

Please find the solution as attached.

anurag356 · Answer

Approach 1

Lets say 2y+Z=180 (supplementary angles). Therefore Z= 180-2y.

Now using exterior angles theorem we can x+5x=Z
Therefore x+5x=180-2y

Also now we can say (x+5x)+2x+5=180 (supplementary angles of trapezium) 
Therefore 6x +2x+5=180

But this gives a different solution as compared to this approach.

Approach 2
In which we take 5x+(2x+5)=180 ( Supplementary angles of parallelogram).
and so on

As per the book this is the solution.

What is wrong with the first approach ?

King407 · Answer

Hi,

Angle Z and 2x+5 aren't the supplementary angle pairs.

Clearly, as you can also see from the figure, both Z and 2x+5 are obtuse angles, their sum will always be more than 180.

The property states that the adjacent angles of a trapezoid are supplementary, which means 2x+5 is supplementary with the angle at the top right corner of the trapezoid.

Similarly, Angle Z is supplementary with top left corner angle of the trapezoid

anurag356 · Answer

Thanks buddy....I did not know that .....Should have seen the diagram more carefully.

pacifist85 · Answer

Hello,

I have been trying to solve this problem for about an hour.
I am going in circles, always ending in sth like 360=360 or 6x+2y=180, which is of course given.

I am sure I am missing sth obvious, but I won't be able to relax until I have seen the solution to this problem!!!

Can someone please post the solution?

anurag356 · Answer

In the above diagram we are given a parallelogram.

We know 5x+(2x+5)= 180
Supplementary angles of a parallelogram

Therefore 7x+5=180
7x=175
x= 25

Now 5x+x+2y=180
Sum of all angles of a triangle is 180

We know x=25
5(25)+25+2y=180
2y=180-150
2y=30
y=15

Kudos if it helps

Bunuel · Answer

https://gmatclub.com/forum/download/file.php?id=27063

In the parallelogram above, what is the value of y?

A) 10 
B) 15 
C) 20
D) 35
E) 45

You should know 3 properties:
1. Consecutive angles in a parallelogram are supplementary, add to 180°.
2. The interior angles of a triangle always add up to 180°.

From (1): 5x + (2x + 5) = 180° --> x = 25°.
From (2): 5x + x + 2y = 6x + 2y = 150 + 2y = 180° --> y = 15°.

Answer: B.

adityadon · Answer

Hey , Whenever you see parallelogram and asked to find angles , check for two angles at end of one side . their sum is going to be 180 . (this is because parallelgram is nothing but set of parallel lines cut by two lines. )
For example in above question , 5x +2x+5 = 180 u get , x= 25 here now u can easily find Y.

Hope this helps

bumpbot · Answer

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In the parallelogram above, what is the value of y?

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In the parallelogram above, what is the value of y?

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