Question

which angle is coterminal with -145°? 215° 625° -405°

Explanation:

Step1: Recall the formula for coterminal angles

Coterminal angles can be found using the formula $\theta + 360^{\circ}n$, where $n$ is an integer.

Step2: Check for $n = 1$

For $\theta=- 145^{\circ}$ and $n = 1$, we calculate $-145^{\circ}+360^{\circ}\times1$.
$$-145^{\circ}+360^{\circ}=215^{\circ}$$

Step3: Check for $n = 2$

For $\theta=-145^{\circ}$ and $n = 2$, we calculate $-145^{\circ}+360^{\circ}\times2$.

$$-145^{\circ}+720^{\circ}=575^{\circ} eq625^{\circ}$$

Step4: Check for $n=-1$

For $\theta=-145^{\circ}$ and $n=-1$, we calculate $-145^{\circ}+360^{\circ}\times(-1)$.

$$-145^{\circ}-360^{\circ}=-505^{\circ} eq - 405^{\circ}$$

Answer:

$215^{\circ}$