# Quiz Question

### 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.

## 8 thoughts on “Quiz Question”

1. Steven Breed says:

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.

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

2. pg13 says:

45 degrees from (59 deg – 14 deg)