In a rhombus ABCD, if ∠ ACB = 40˚, then find ∠ ADB.

To Find: ∠ ADB

Given: ABCD is a rhombus and ∠ACB = 40˚

Concept Used:

Diagonals of a rhombus bisect at the right angle.

Sum of angles of a triangle = 180˚

SAS Congruence: If two sides and one angle of a triangle is equal to two sides and angle of another triangle then the two triangles are said to be congruent.

Diagram:

Explanation:

∠BOC = 90˚

In Δ BOC,

∠BOC + ∠ACB +∠ CBD = 180˚

90˚ + 40˚ + ∠CBD = 180˚

∠CBD = 180˚ - 30˚

∠CBD = 50˚

Now,

In Δ BOC and Δ AOD, we get,

AD = BC [All sides of rhombus are equal]

AO = OC [ Diagonals of a rhombus bisect each other]

OD = OB [Diagonals of a rhombus bisect each other]

Therefore,

Δ BOC and Δ AOD are congruent by SAS congruence.

Now,

∠ADB = 50˚ [By C.P.C.T]

Hence, ∠ADB = 50˚.