An angle whose measure is greater than 180^° but strictly less than 360^° is defined as a reflex angle. Since 275^° falls within this range, it is classified as a reflex angle.

In standard position on the Cartesian plane, the four quadrants span from 0^° to 90^° for Quadrant I, 90^° to 180^° for Quadrant II, 180^° to 270^° for Quadrant III, and 270^° to 360^° for Quadrant IV. Because 275^° is greater than 270^° and less than 360^°, its terminal arm lies in the fourth quadrant.

In standard position on the Cartesian plane, the four quadrants span from 0^° to 90^° for Quadrant I, 90^° to 180^° for Quadrant II, 180^° to 270^° for Quadrant III, and 270^° to 360^° for Quadrant IV. Because 275^° is greater than 270^° and less than 360^°, its terminal arm lies in the fourth quadrant.

What angle did 275 degree make

Answer: $275^\circ$ is a reflex angle that lies in Quadrant IV in standard position, with an acute reference angle of $85^\circ$ .

Step-by-step solution

Step 1: Classify the angle by measure

An angle whose measure is greater than $180^\circ$ but strictly less than $360^\circ$ is defined as a reflex angle. Since $275^\circ$ falls within this range, it is classified as a reflex angle.

Step 2: Determine the quadrant in standard position

In standard position on the Cartesian plane, the four quadrants span from $0^\circ$ to $90^\circ$ for Quadrant I, $90^\circ$ to $180^\circ$ for Quadrant II, $180^\circ$ to $270^\circ$ for Quadrant III, and $270^\circ$ to $360^\circ$ for Quadrant IV. Because $275^\circ$ is greater than $270^\circ$ and less than $360^\circ$ , its terminal arm lies in the fourth quadrant.

Step 3: Calculate the reference angle

For an angle $\theta$ terminating in Quadrant IV, the reference angle is the acute angle made with the positive $x$ -axis, calculated as $360^\circ - \theta$ . Here, $360^\circ - 275^\circ = 85^\circ$ .

Solve your own maths question free →