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netineya [11]
3 years ago
7

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

Mathematics
1 answer:
Naddik [55]3 years ago
8 0

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:

\theta_{c} = \theta_{o} + 360\cdot i, i \in \mathbb{Z} (1)

Where:

\theta_{o} - Original angle, in sexagesimal degrees.

\theta_{c} - Coterminal angle, in sexagesimal degrees.

i - Coterminal angle index, no unit.

If we know that \theta_{o} = -215^{\circ} and i = 1, then the coterminal angle that is less than 360° is:

\theta_{c} = -215^{\circ} + 360\cdot (1)

\theta_{c} = 145^{\circ}

The positive angle less than 360° that is coterminal with -215° has a measure of 145°.

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