In the given figure ABCD is a rhombus, the value of x is.

50°

The correct answer is Option 2: 50°

In rhombus ABCD:

Properties of a rhombus

1. Opposite angles are equal.
2. Adjacent angles are supplementary (sum = $180^\circ$).
3. Diagonals bisect the vertex angles.

Step 1: Find angle A

Diagonal AC bisects $\angle A$.

Given:

$\angle BAC = 40^\circ$

So,

$\angle A = 2 \times 40^\circ = 80^\circ$

Step 2: Find angle D

Adjacent angles in a rhombus are supplementary:

$\angle D = 180^\circ - 80^\circ = 100^\circ$

Step 3: Use diagonal property

Diagonal BD bisects $\angle D$.

$x = \frac{100^\circ}{2} = 50^\circ$