Question

the angles with measures 0° < θ < 90° are located in the quadrant choose your answer... the angles with measures 90° < θ < 80° are located in quadrant choose your answer... the angles with measures 180° < θ < 270° are located in quadrant choose your answer... the angles with measures 270° < θ < 360° are located in quadrant choose your answer...

Explanation:

1. Angles between \(0^\circ\) and \(90^\circ\) lie in the first quadrant, where both \(x\) and \(y\) coordinates are positive.
2. The second question has a typo; the correct range is \(90^\circ < \theta < 180^\circ\), which corresponds to the second quadrant (positive \(y\), negative \(x\)).
3. Angles between \(180^\circ\) and \(270^\circ\) lie in the third quadrant, where both \(x\) and \(y\) coordinates are negative.
4. Angles between \(270^\circ\) and \(360^\circ\) lie in the fourth quadrant, where \(x\) is positive and \(y\) is negative.

Answer:

1. The angles with measures \(0^\circ < \theta < 90^\circ\) are located in the quadrant: Quadrant I
2. The angles with measures \(90^\circ < \theta < 180^\circ\) are located in quadrant: Quadrant II
3. The angles with measures \(180^\circ < \theta < 270^\circ\) are located in quadrant: Quadrant III
4. The angles with measures \(270^\circ < \theta < 360^\circ\) are located in quadrant: Quadrant IV