How do I prove that Psi (the orange angle) is 90°. I know or can calculate all the blue angles I marked but I don´t know what equation I need to prove to show that Psi is 90°.

Question

anonymous · Answer

Here is the picture with the angles I mentioned.

anonymous · Answer

It seems easy because I know so many angles but yet I don´t know how to formulate the mathematical condition for psi to equal 90°.

phi · Answer

You have to find the angles labeled 1,2 and 3.  and add them up. You have to be careful of the signs.  Let a clockwise turn be positive and c c w be negative.

phi · Answer

I think angle 1 is alpha - beta

phi · Answer

angle 2 is phi + 90 - rho

anonymous · Answer

I have the same angle 1 but for angle2 I got 180-2*rho.

phi · Answer

hopefully 180 - 2*rho is the same as phi+90 - rho

anonymous · Answer

Hopefully. Although I don´t know why I have to look out for the sign of the angle. Why does it matter if the angle is created counterclockwise or clockwise?

phi · Answer

|dw:1385215356950:dw|