### One of a continuing series

Mathematics again. What is the value of the indicated angle? Post your answer as a comment below.

## Update

Three people have submitted correct answers, all holding Ph.D. degrees, but none in mathematics. Here is my solution, which I believe to be the simplest approach. See the diagram:

It’s the same as the original diagram, but I have added some labels, and I have added line **BC**.

Notice immediately that **BC** is the same as **AB**. If you don’t notice this immediately, then stop reading now and get into another line of work. Now notice that angle **BAD** is the same as angle **EBC**. Again, if you don’t notice, stop reading. **BAD** = **EBC** implies **ABC** is a right angle. Again, you can quit while you’re ahead. We have a right isosceles triangle, which means that **BAC** is 45°. And no mental gymnastics have been required.

The first way that comes to my mind is to use the formula for the tangent of an angle difference, i.e., tan(x-y) = (tanx-tany)/(1+tanx*tany). The values of tanx and tany are computed from counting the squares in the legs of each triangle. Then use arctan to get x-y.

Steve, It’s easier than that.

It may be easier than that, as you described, but the arctan method is straightforward and will work for the general case.

45 degrees from (59 deg – 14 deg)

Prasad,

Where did you get the 59 and 14? It’s not even necessary to do that. The answer is obvious by looking at the diagram.

The answer is 45 degrees: the triangle formed by placing a line segment between the two vertices that are not connected is a right Isosceles triangle. It would be a lot easier to explain why the new triangle is Isosceles, and a right Isosceles triangle at that, if I drew this out (since there are no labels on the original diagram), but I’m to lazy to do that.

… and before you complain about the “to” that should be a “too”, I’ll just point out that it’s good enough for our President so shut up!

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