#### Answer

$-\dfrac{\sqrt 2}{2}$

#### Work Step by Step

The reference angle of an angle $0 \leq \theta \lt 2\pi $ based on its position can be computed by using the following steps:
a) Quadrant- I: $\theta $
b) Quadrant -II: $(\pi-\theta)$
c) Quadrant- III: $(\theta - \pi)$
d) Quadrant - IV: $(2\pi - \theta)$
Thus, we have the reference angle $540^{\circ}-495^{\circ}=45^{\circ}$
So, $\cos 45^{\circ}=\dfrac{\sqrt 2}{2}$
Thus, we have $\cos 495^{\circ}=-\dfrac{\sqrt 2}{2}$ because $\theta $ lies in Quadrant-II.