I'm having trouble about deciding the initial angle theta before drawing the Mohr's circle. From what I've learned from the lecture, I need to draw a normal line of indicated plane and find the angle between the x axis and the normal line. Which gives me 150 degree from the first pic and 115 degree from the second pic. And after that, I need to double these angle to put them in the Mohr's Circle, which is 300 and 230 respectively. But the solution speaks otherwise of problem 17. There weren't any normal line and it just doubled the angle right away. From my point of view, these two situations are conceptually same. I don't understand what's the difference. Any explanations would be greatly appreciated.
There are two different angle $\theta$'s. one is the normal stress angle $\theta_p $between the stress axis, X, and point a(x,s) on the mohr circle.
The other is shear stress angle $\theta_s$ from the shear axis with a positive direction down and the sense of the angle is from the shear axis to point a(x,s).
here is a site that explains how to build the mohr circle. linkhere