Question

which statement is not correct?
a. the terminal side of a 145° angle is in quadrant ii.
b. a 75° angle is an acute angle.
c. a 185° angle is an obtuse angle.
d. a 225° angle is a reflex angle.

Explanation:

Step1: Recall angle definitions

• Quadrant II: \(90^\circ < \theta < 180^\circ\); Acute: \(0^\circ < \theta < 90^\circ\); Obtuse: \(90^\circ < \theta < 180^\circ\); Reflex: \(180^\circ < \theta < 360^\circ\).

Step2: Analyze Option A

\(90^\circ < 145^\circ < 180^\circ\), so terminal side in Quadrant II. Correct.

Step3: Analyze Option B

\(0^\circ < 75^\circ < 90^\circ\), so acute angle. Correct.

Step4: Analyze Option C

\(185^\circ > 180^\circ\), obtuse angles are \(90^\circ < \theta < 180^\circ\). So \(185^\circ\) is not obtuse. Incorrect.

Step5: Analyze Option D

\(180^\circ < 225^\circ < 360^\circ\), so reflex angle. Correct.

Answer:

C. A \(185^\circ\) angle is an obtuse angle.