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Quadrilaterals — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSQuadrilaterals1 Mark
Question
Write the correct answer in the following:
ABCD is a rhombus such that $\angle\text{ACB}=40^\circ.$ then $\angle\text{ADB}$ is:
✓

Answer

  1. 50º
    Solution:
    ABCD is a rhombus such thet $\angle\text{ACB}=40^\circ.$
    We know that diagonnals of rhombus bisect each other right angles.
    In right $\Delta\text{BOC},$ we have

    $\angle\text{OBC}=180^\circ-(\angle\text{BOC}+\angle\text{BCO})$ (angle sum property)
    $=180^\circ-(90^\circ+40^\circ)=50^\circ$
    $\therefore\ \angle\text{DBC}=\angle\text{OBC}=50^\circ$
    Now,
    $\angle\text{ADB}=\angle\text{DBC}$ [Alt. int. $\angle\text{s}$ ]
    $\therefore\ \angle\text{ADB}=50^\circ[\therefore\angle\text{DBC}=50^\circ]$
    Hence, (c) is the correct answer.

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