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Circles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsCircles1 Mark
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Answer

  1. 50º
    Solution:

    Let AB and CD intersect at O. Then In the triangle ACO,
    $\angle\text{A}+\angle\text{C}+\angle\text{D}=180^\circ$
    $40^\circ+\angle\text{C}+90^\circ=180^\circ$
    $130^\circ+\angle\text{C}=180^\circ$
    $\angle\text{C}=50^\circ$
    As per the theorem, Angles in the same segment of a circle are equal.
    Hence, $\angle\text{ABD}=\angle\text{C}=50^\circ$

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