For an angle, what does it mean to be bounded away 90 degrees?

Question

Nocedal and Wright, in their book Numerical Optimization, just above (3.17), use this wording:

...the angle $\theta_k$ is bounded away from $90^\circ$,...

what does this mean?

Answer 1

It means: there exists some $\phi>0$ such that $|\theta-90|>\phi$.