Answer:
The positive angle less than 360° that is coterminal with -215° has a measure of 145°.
Step-by-step explanation:
From Geometry, we know that angles form a family of coterminal angles as function of number of revolutions done on original angle. We can represent the set of all coterminal angles by means of the following expression:
[tex]\theta_{c} = \theta_{o} + 360\cdot i[/tex], [tex]i \in \mathbb{Z}[/tex] (1)
Where:
[tex]\theta_{o}[/tex] - Original angle, in sexagesimal degrees.
[tex]\theta_{c}[/tex] - Coterminal angle, in sexagesimal degrees.
[tex]i[/tex] - Coterminal angle index, no unit.
If we know that [tex]\theta_{o} = -215^{\circ}[/tex] and [tex]i = 1[/tex], then the coterminal angle that is less than 360° is:
[tex]\theta_{c} = -215^{\circ} + 360\cdot (1)[/tex]
[tex]\theta_{c} = 145^{\circ}[/tex]
The positive angle less than 360° that is coterminal with -215° has a measure of 145°.
