Q. 94.5( 12 Votes )

In a rhombu

Answer :

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˚.


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