Question

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

Options

•  70°

• 45°

• 50°

• 60°

Answer 1

Rhombus ABCD is given as follows:

It is given that∠ACB = 40°.

Therefore, ∠OCB = 40° (Because O lies on AC)

We know that the diagonals of a rhombus intersect at right angle.

Therefore, ∠BOC = 90°

By angle sum property of a triangle, we get:

∠CBO + ∠OCB + ∠BOC = 180°

        ∠CBO + 40° + 90° = 180°

                ∠CBO+ 130° = 180 °

                          ∠CBO = 50°

Since, O lies on BD

 ∠CBD = 50°

Also , CB || DA

Therefore,

∠ADB = ∠CBD

 ∠ADB = 50°

Hence, the correct choice is (c).