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Quadrilaterals — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSQuadrilaterals1 Mark
Question
In a rhombus ABCD, if $\angle\text{ACB} = 40^\circ,$ then $\angle\text{ADB} =\ ?$
✓

Answer

  1. 50º
    Solution:

    Given ABCD is a rhombus. Diagonals bisect each other perpendicularly.
    Hence $\angle\text{BOC} = 90^\circ$
    Given $\angle\text{OCB} = 40^\circ$
    $\text{AD || BC}$ and BD is the transversal
    $∴ \angle\text{ADB} = \angle\text{DBC}$ (Alternate angles)
    Hence in right angled $\triangle\text{BOC},$
    $\angle\text{BOC} + \angle\text{OCB} + \angle\text{OBC} = 180^\circ$
    $⇒ 90^\circ + 40^\circ + \angle\text{OBC} = 180^\circ$
    $⇒130^\circ + \angle\text{OBC} = 180^\circ$
    $⇒ \angle\text{OBC} = 180^\circ - 130^\circ = 50^\circ$
    But $\angle\text{OBC} = \angle\text{DBC}$
    Therefore, $\angle\text{ADB} = 50^\circ.$

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