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abcd is quadrilateral in which z/y=y/x=x/w=k and k is an integer. also w,x90, then the difference between the greatest angle and the smallest angle is

abcd is quadrilateral in which z/y=y/x=x/w=k and k is an integer. also w,x90, then the difference between the greatest angle and the smallest angle is

Grade:11

1 Answers

Vikas TU
14149 Points
5 years ago
If k = 1, then w,x 90 would be impossible, so obviously k is not 1. 

If k >= 3, then y > 90 would mean z > 270, so y+z > 360, which is impossible (since x+y+z+w=360), so k must be less than 3. 

In other words, k = 2 is the only possible integer. 

That's the hardest part. Now we can just write all the angles in terms of w: 
x = 2w 
y = 2x = 4w 
z = 2y = 8w 

Then 
x+y+z+w = 360 
2w + 4w + 8w + w = 360 
15w = 360 
w = 24 

Lastly, 
z = 8w = 196 
and therefore 
z-w = 196 - 24 = 172.

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