Find an angle in each quadrant with a common reference angle with $296^{\circ}$, from $0^{\circ} \leq \theta< 360^{\circ}$
Answer
Final Answer: The angles in each quadrant with a common reference angle with \(296^\circ\) are \(64^\circ\), \(116^\circ\), \(244^\circ\), and \(296^\circ\). So, the final answer is \(\boxed{64^\circ, 116^\circ, 244^\circ, 296^\circ}\).
Step 1 ：Given the angle \(\theta = 296^\circ\), which is in the fourth quadrant.
Step 2 ：To find the reference angle, subtract the given angle from 360 degrees. So, the reference angle is \(360^\circ - 296^\circ = 64^\circ\).
Step 3 ：An angle in the first quadrant with the same reference angle is simply the reference angle itself, so \(\text{angle}_{q1} = 64^\circ\).
Step 4 ：An angle in the second quadrant with the same reference angle is found by subtracting the reference angle from 180 degrees, so \(\text{angle}_{q2} = 180^\circ - 64^\circ = 116^\circ\).
Step 5 ：An angle in the third quadrant with the same reference angle is found by adding the reference angle to 180 degrees, so \(\text{angle}_{q3} = 180^\circ + 64^\circ = 244^\circ\).
Step 6 ：An angle in the fourth quadrant with the same reference angle is the given angle, so \(\text{angle}_{q4} = 296^\circ\).
Step 7 ：Final Answer: The angles in each quadrant with a common reference angle with \(296^\circ\) are \(64^\circ\), \(116^\circ\), \(244^\circ\), and \(296^\circ\). So, the final answer is \(\boxed{64^\circ, 116^\circ, 244^\circ, 296^\circ}\).
