Q. 94.5( 12 Votes )
In a rhombu
To Find: ∠ ADB
Given: ABCD is a rhombus and ∠ACB = 40˚
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.
∠BOC = 90˚
In Δ BOC,
∠BOC + ∠ACB +∠ CBD = 180˚
90˚ + 40˚ + ∠CBD = 180˚
∠CBD = 180˚ - 30˚
∠CBD = 50˚
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]
Δ BOC and Δ AOD are congruent by SAS congruence.
∠ADB = 50˚ [By C.P.C.T]
Hence, ∠ADB = 50˚.
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