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Circles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsCircles1 Mark
MCQ
ABCD is a cyclic quadrilateral such that $\angle\text{ADB} = 30^\circ$ and $\angle\text{DCA} = 80^\circ,$ then $\angle\text{DAB} =$
  • A
    70°
  • B
    100°
  • C
    125°
  • D
    150°
✓

Answer

  1. 70°
    Solution:

    ABCD is a cyclic Quadrilateral.
    Consider $\triangle\text{ABD}$ and $\triangle\text{ABC}.$
    Both are on the same base AB and $\angle\text{ADB}$ and $\angle\text{ACB}$ are the angles in the same segment AB.
    $\Rightarrow\angle\text{ADB}=\angle\text{ACB}=30^\circ$
    $\Rightarrow\angle\text{BCD}=80^\circ+30^\circ=110^\circ$
    In a cyclic Quadrilateral, sum of opposite angles is 180°
    $\Rightarrow\angle\text{A}+\angle\text{C}=180^\circ$
    $\Rightarrow\angle\text{DAB}+\angle\text{BCD}=180^\circ$
    $\Rightarrow\angle\text{DAB}=180^\circ-110^\circ=70^\circ$

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