ABCD is a parallelogram in which ∠BAD = 60° and ∠BAC = 30°, then ∠CBD =

1. 45°

2. 60°

3. 70°

4. 80°

Given,

∠BAD = 60° and ∠BAC = 30°.

From figure,

∠CAD = ∠BAD - ∠BAC = 60° - 30° = 30°.

If diagonal of a parallelogram bisects a vertex angle, then it is a rhombus.

Thus, ABCD is a rhombus.

In rhombus adjacent angles are supplementary.

Thus,

∠BAD + ∠CBA = 180°

60° + ∠CBA = 180°

∠CBA = 180° - 60° = 120°.

Since, diagonals of rhombus bisect the vertex angle,

∴ ∠CBD = $\dfrac{∠CBA}{2} = \dfrac{120°}{2}$ = 60°.

Hence, option 2 is the correct option.