# How do you determine the quadrant in which the angle 257^circ30' lies?

Feb 5, 2017

Angle ${257}^{\circ} 30 '$ lies in Q3.

#### Explanation:

First quadrant Q1 is ${0}^{\circ}$ to ${90}^{\circ}$

Second quadrant Q2 is ${90}^{\circ}$ to ${180}^{\circ}$

Third quadrant Q3 is ${180}^{\circ}$ to ${270}^{\circ}$

and fourth quadrant Q4 is ${270}^{\circ}$ to ${360}^{\circ}$

Hence as ${257}^{\circ} 30 '$ lies between ${180}^{\circ}$ and ${270}^{\circ}$

Angle ${257}^{\circ} 30 '$ lies in Q3.