Inside the triangle one of the angle should be 50 (alternate angle )

Then 50+40 = 90

and 180-90 =90 so answer is 90. ]]>

What gets me is that before calculating I tried to think what I expected the answer to be, and came out with one-third, and I don’t know why that sounded right. I’m curious whether I had encountered the problem before and remembered the answer without remembering it, or whether there’s some obvious way to see it that my conscious mind isn’t noticing. Or if the lazy part of my mind figured the answer must be some nice simple fraction, and 1/2 is right out, and 1/4 looks too small, so 1/3 is the only plausible choice because this kind of setup never gives you a 2/5th or a 3/7th or something like that.

]]>x +1/4 +1/2 – (1/4)x = 1

(3/4)x = 1/4

x = 1/3

]]>Conceptually, finding equivalent ratios is identical to equivalent fractions

]]>Thanks for your solution. I came across this as I wanted to verify my answer as well.

Here’s my methodology.

First you can’t assume larger rectangles mean larger areas (example: the 14 rectangle is larger than the 15).

Second, since we have 16 smaller rectangles, you can assume that the lines dividing rows and columns are parallel. As such, the ratio of areas of rectangles should be equal.

Third, I used the above for pairs of adjacent rectangles. The first pair I used was the 20 and 14. This means each of the pairs of rectangles in the 2nd and 3rd column should have the same ratio. Thus the “dy” (according to your row and column labels) rectangle has an area of 17.5

Similarly, using the 12 and 8 rectangles yield 22.5 for the “by” rectangle.

Finally, using the same method on the “by”, “bz”, “dy”, and “dz” rectangles gives us 27 for the unknown as required.

Sorry, just noticed someone has already posted a ratio related response and I’m about 7 months too late!

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