Solve for x :

$cos\Big(\dfrac{x}{2} + 10°\Big)$ = $\dfrac{\sqrt3}{2}$

$\text{cos}\Big(\dfrac{x}{2} + 10°\Big)$ = $\dfrac{\sqrt3}{2}$

$⇒ \text{cos } \Big(\dfrac{x}{2} + 10°\Big) = \text{cos 30°}$

So,

$⇒ \Big(\dfrac{x}{2} + 10°\Big) = 30°\\[1em] ⇒ \dfrac{x}{2} = 30° - 10°\\[1em] ⇒ x = 20° \times 2\\[1em] ⇒ x = 40° \\[1em]$

Hence, x = 40°.