Question

which angle is coterminal with 170°? -450° -350° -190°

Explanation:

Step1: Recall coterminal angle formula

Coterminal angles differ by multiples of \(360^\circ\). So, for an angle \(\theta\), coterminal angles are \(\theta + 360^\circ k\) or \(\theta - 360^\circ k\) where \(k\) is an integer.

Step2: Test each option

• For \(-450^\circ\): Let's see if \(-450^\circ + 360^\circ k = 170^\circ\). Try \(k = 2\): \(-450 + 720 = 270

eq170\). \(k = 1\): \(-450 + 360=-90
eq170\).

• For \(-350^\circ\): Try \(k = 1\): \(-350 + 360 = 10

eq170\). \(k = 2\): \(-350+720 = 370
eq170\).

• For \(-190^\circ\): Try \(k = 1\): \(-190+360 = 170\). Yes, this works.

Answer:

\(-190^\circ\) (the third option, \(-190^\circ\))