Question

Which quadrant $$180<\theta <270$$ degree lies?

Answer 1

Hint: Degree measurement is based on a circle, which is $${360}^0$$. If a ray is allowed to rotate one complete revolution counter clockwise around the $$xy$$ plane, starting and ending at the positive $$x-axis$$, we say that the ray has rotated $${360}^0$$, Its angle measurement would be written $${360}^0$$

                     

Complete Step-by-step solution
Here the given angle is$${180}^0<\theta <{270}^0$$.
We have the following angle represents in Quadrants:
Quadrant I $$=0^0<\theta <{90}^0$$
Quadrant II $$={90}^0<\theta <{180}^0$$
Quadrant III $$={180}^0<\theta <{270}^0$$
Quadrant IV $$={270}^0<\theta <{360}^0$$
i.e. this lies in Quadrant III as the range of quadrant III is $$={270}^0<\theta <{360}^0$$
Initial line: negative $$x-axis$$
Terminal line: negative $$y-axis$$

Note: Now let us know look into the concept to make the concept of quadrants simple., i.e. for Quadrant I: -initial side: positive $$x-axis$$
Terminal side: Positive $$y-axis$$
Counter-clockwise rotation
We swept angle between $$0^0$$to$${90}^0$$