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Lines and Angles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsLines and Angles1 Mark
MCQ
Two straight lines AB and CD intersect one another at the point O. If $\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}=274^\circ,$ then $\angle\text{AOD}=$
  • A
    86°
  • B
    90°
  • C
    94°
  • D
    137°
✓

Answer

  1. 86°
    Solution:

    $\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}+\angle\text{AOD}=360^\circ\dots(1)$
    Now,
    $\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}=274^\circ\dots(2)$ [Given]
    From (1) and (2).
    $274^\circ+\angle\text{AOD}=360^\circ$
    $\Rightarrow\ \angle\text{AOD}=360^\circ-274^\circ$
    $\Rightarrow\ \angle\text{AOD}=86^\circ$

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