Hello, BrainMan!

The proof is simple in one direction . . .

An angle θ such that 0° < θ < 90°

can be constructed with a ruler if and only iftan θis a rational number.

If is a rational number , where are positive integers,

. . we can construct angle

Code:* R * | * | * | a * | * θ | - - * - - - - - - - - * - - P b Q

On a horizontal line, mark pointsPandQso that:PQ = b

AtQ, erect a perpendicularQRso that:QR = a

Draw line segmentPR.

. . Then: ./RPQ = θ