The given equations are √3x+y = 1 ... (i)
x + √3y = 1... (ii)
Since we have to find an angle between the two lines i.e., firstly we have to find the slopes of (i) and (ii).
Slope of (i) = m1 = - √3 ... (iii)
Slope of (ii) = m2 = −

1

√3

... (iv)
Let θ be an angle between the given two lines, then
tan θ = |

m1−m2

1+m1m2

| = |

−√3−(− 1 √3 )

1+(−√3).(− 1 √3 )

| (from (iii) & (iv))
= |

−√3+ 1 √3

1+1

| = |

(−3+1)

2√3

| = |

−1

√3

| =

1

√3

⇒ tan θ =

1

√3

⇒ tan θ = tan 30° ⇒ θ = 30°
∴ The angle between the two given lines is 30° and the other angle is 180° – 30° = 150°.