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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 $\angle\text{ADB}=$
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Answer

  1. 50°
    Solution:

    Consider $\triangle\text{AOD} \ \&\ \triangle\text{COB}$ $$
    $\angle\text{AOD}=\angle\text{COB}=90^\circ$
    AD = BC (Sides of Rhombus)
    AO = CO (Diagonals bisects each other)
    So by RHS property, $\triangle\text{AOD}\cong\triangle\text{COB}$
    $\Rightarrow\angle\text{OAD}=\angle\text{OCB}=40^\circ$
    $\angle\text{ADB}=\angle\text{ADO}=180^\circ-90^\circ-40^\circ=50^\circ$

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