Question

draw the angle with the given measure in standard position.

1. -340°
2. 150°
3. -185°
4. 300°

Explanation:

Step1: Recall standard - position rules

An angle in standard position has its vertex at the origin and its initial side on the positive x - axis. Positive angles are measured counter - clockwise and negative angles are measured clockwise.

Step2: Draw \(-340^{\circ}\)

Since \(-340^{\circ}=-360^{\circ}+ 20^{\circ}\), start at the positive x - axis and rotate \(340^{\circ}\) clockwise. This is equivalent to a \(20^{\circ}\) counter - clockwise rotation.

Step3: Draw \(150^{\circ}\)

Start at the positive x - axis and rotate \(150^{\circ}\) counter - clockwise. The terminal side will be in the second quadrant.

Step4: Draw \(-185^{\circ}\)

Start at the positive x - axis and rotate \(185^{\circ}\) clockwise. Since \(185^{\circ}=180^{\circ}+5^{\circ}\), the terminal side will be in the third quadrant, just \(5^{\circ}\) past the negative x - axis.

Step5: Draw \(300^{\circ}\)

Start at the positive x - axis and rotate \(300^{\circ}\) counter - clockwise. Since \(300^{\circ}=360^{\circ}-60^{\circ}\), the terminal side will be in the fourth quadrant, \(60^{\circ}\) away from the positive x - axis in the counter - clockwise direction.

To actually draw these angles:

1. For \(-340^{\circ}\): Draw a ray starting from the origin and making a \(20^{\circ}\) angle with the positive x - axis in the counter - clockwise direction.
2. For \(150^{\circ}\): Draw a ray starting from the origin and making a \(150^{\circ}\) angle with the positive x - axis in the counter - clockwise direction. The ray should be in the second quadrant.
3. For \(-185^{\circ}\): Draw a ray starting from the origin and making a \(185^{\circ}\) clockwise rotation from the positive x - axis. The ray should be in the third quadrant.
4. For \(300^{\circ}\): Draw a ray starting from the origin and making a \(300^{\circ}\) counter - clockwise rotation from the positive x - axis. The ray should be in the fourth quadrant.

There is no single numerical answer for drawing angles. The task is to accurately represent the angles in the coordinate - plane as described above.

Answer:

Step1: Recall standard - position rules

An angle in standard position has its vertex at the origin and its initial side on the positive x - axis. Positive angles are measured counter - clockwise and negative angles are measured clockwise.

Step2: Draw \(-340^{\circ}\)

Since \(-340^{\circ}=-360^{\circ}+ 20^{\circ}\), start at the positive x - axis and rotate \(340^{\circ}\) clockwise. This is equivalent to a \(20^{\circ}\) counter - clockwise rotation.

Step3: Draw \(150^{\circ}\)

Start at the positive x - axis and rotate \(150^{\circ}\) counter - clockwise. The terminal side will be in the second quadrant.

Step4: Draw \(-185^{\circ}\)

Start at the positive x - axis and rotate \(185^{\circ}\) clockwise. Since \(185^{\circ}=180^{\circ}+5^{\circ}\), the terminal side will be in the third quadrant, just \(5^{\circ}\) past the negative x - axis.

Step5: Draw \(300^{\circ}\)

Start at the positive x - axis and rotate \(300^{\circ}\) counter - clockwise. Since \(300^{\circ}=360^{\circ}-60^{\circ}\), the terminal side will be in the fourth quadrant, \(60^{\circ}\) away from the positive x - axis in the counter - clockwise direction.

To actually draw these angles:

1. For \(-340^{\circ}\): Draw a ray starting from the origin and making a \(20^{\circ}\) angle with the positive x - axis in the counter - clockwise direction.
2. For \(150^{\circ}\): Draw a ray starting from the origin and making a \(150^{\circ}\) angle with the positive x - axis in the counter - clockwise direction. The ray should be in the second quadrant.
3. For \(-185^{\circ}\): Draw a ray starting from the origin and making a \(185^{\circ}\) clockwise rotation from the positive x - axis. The ray should be in the third quadrant.
4. For \(300^{\circ}\): Draw a ray starting from the origin and making a \(300^{\circ}\) counter - clockwise rotation from the positive x - axis. The ray should be in the fourth quadrant.

There is no single numerical answer for drawing angles. The task is to accurately represent the angles in the coordinate - plane as described above.