In a rhombus ABCD, if ∠ACB = 40°, then ∠ADB = ?

Correct option is B

Given:

Rhombus ABCD

∠ACB = 40°

Formula Used:

In a rhombus, the diagonals bisect the interior angles.

In a rhombus, all sides are equal.

If all sides of a triangle are equal, then it is an isosceles triangle, and the angles opposite to the equal sides are also equal.

The sum of the interior angles of a triangle is 180°.

Solution:

Since ABCD is a rhombus, sides AB = BC.

Therefore, triangle ABC is an isosceles triangle.

∠ACB = 40° (Given)

Since triangle ABC is isosceles, ∠BAC = ∠BCA = 40°

The sum of angles in triangle ABC is 180°.

∠ABC + ∠BAC + ∠ACB = 180°

∠ABC + 40° + 40° = 180°

∠ABC = 180° - 80° = 100°

In a rhombus, the diagonals bisect the interior angles.

Diagonal BD bisects ∠ABC, so ∠ABD = $$\frac{∠ABC } 2 = \frac{100° }2 = 50$$​°

In Triangle ADB, AB = AD (sides of a Rhombus)

Therefore, ∠ADB = ∠ABD = 50°

Therefore, ∠ADB = 50°.