Answer :
To determine the measure of an angle that is coterminal with a \(300^{\circ}\) angle using the given expressions, let's calculate the difference between \(300^{\circ}\) and each of the given expressions.
A coterminal angle is an angle that, when multiplied by a full rotation (i.e., \(360^{\circ}\)), results in an angle that is either positive or negative equivalent to the original angle:
1. \(300^{\circ} - 860^{\circ}\)
[tex]\[ 300^{\circ} - 860^{\circ} = -560^{\circ} \][/tex]
2. \(300^{\circ} - 840^{\circ}\)
[tex]\[ 300^{\circ} - 840^{\circ} = -540^{\circ} \][/tex]
3. \(300^{\circ} - 740^{\circ}\)
[tex]\[ 300^{\circ} - 740^{\circ} = -440^{\circ} \][/tex]
4. \(300^{\circ} - 720^{\circ}\)
[tex]\[ 300^{\circ} - 720^{\circ} = -420^{\circ} \][/tex]
Thus, the coterminal angles we calculated from the provided expressions are:
1. \(-560^{\circ}\)
2. \(-540^{\circ}\)
3. \(-440^{\circ}\)
4. \(-420^{\circ}\)
These values represent the measures of angles that are coterminal with a [tex]\(300^{\circ}\)[/tex] angle for each of the given expressions.
A coterminal angle is an angle that, when multiplied by a full rotation (i.e., \(360^{\circ}\)), results in an angle that is either positive or negative equivalent to the original angle:
1. \(300^{\circ} - 860^{\circ}\)
[tex]\[ 300^{\circ} - 860^{\circ} = -560^{\circ} \][/tex]
2. \(300^{\circ} - 840^{\circ}\)
[tex]\[ 300^{\circ} - 840^{\circ} = -540^{\circ} \][/tex]
3. \(300^{\circ} - 740^{\circ}\)
[tex]\[ 300^{\circ} - 740^{\circ} = -440^{\circ} \][/tex]
4. \(300^{\circ} - 720^{\circ}\)
[tex]\[ 300^{\circ} - 720^{\circ} = -420^{\circ} \][/tex]
Thus, the coterminal angles we calculated from the provided expressions are:
1. \(-560^{\circ}\)
2. \(-540^{\circ}\)
3. \(-440^{\circ}\)
4. \(-420^{\circ}\)
These values represent the measures of angles that are coterminal with a [tex]\(300^{\circ}\)[/tex] angle for each of the given expressions.
