Question

if k is a half-plane determined by QR, then for every real number 0 < x < or = to 180, there is exactly one ray, QQP, that lies in k such that m < PQR = ______

Answer 1

Let me start from the meaning of half plane.you must have learned that there are two axes X and Y axes which includes positive X axes and negative X axes and there is positive Y axes and negative y axes. So there are four quadrants which i have explained in the figure. I have explained the meaning of Half plane in the Diagram also. Half plane=Figure obtained by covering any two adjacent regions of the coordinate axes.So we get four half planes.

Now your question is k is a half plane determined by QR, such that 0<x≤180 and there is exactly one ray QRP that lies in k

So, $0< \angle PQR \leq 180^\cir{0}$