Let's look at it this way:

At point E, we have 3 angles, E1 = unknown, E2 = a(which we want to know) and E3 = 30. Same goes for D's angles, D1 = unknown, D2 = Unknow, D3 = 40 (calculated).

From Calculations by using simple means of adding and subtracting, we results in E1+E2(a) = 150 and D1+D2 = 140

Therefore, if you give any number to E2(a), the rest will work out mathematically because they'll fit right in.

For example:

If E2(a) = 10, therefore E1 = 150-10 = 140. Then D1 = 180 - (140+20) = 20.

Then D2 = 140-20 = 120.

So for the top triangle, we have 20, 140, 20, and for the middle angle (aka a's triangle), we'll have 120, 10, 50, which mathematically, all added correctly.

Try using any combinations, and they'll come out to match up perfectly.


So the "truest" way to contruct the triangles using the correct measurements and measure the correct angle would be using a ruler and measure it. By using simple addition, subtraction, and subtitution, you can't truly find out the right angle because of the reason explained above.