Question

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

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:

$\theta_{c} = \theta_{o} + 360\cdot i$, $i \in \mathbb{Z}$ (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°.