Question

ABCD is a rhombus such that ∠ACB = 40°, find ∠ADB​

Answer 1

Solution ↓

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

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˚.

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