Find a positive angle less than 360° that is coterminal with the given angle.
- 215°
A positive angle less than 360° that is coterminal with - 215° is

Answers

Answer 1

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°.


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