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Lines and Angles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsLines and Angles1 Mark
MCQ
Two lines AB and CD intersect at O. If $\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}=270^\circ,$then $\angle\text{AOC}=$
  • A
    70°
  • B
    80°
  • C
    90°
  • D
    180°
✓

Answer

  1. 90°
    Solution:

    $\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}=270^\circ$ [Given]
    From figure,
    $\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}+\angle\text{DOA}=360^\circ$
    $\Rightarrow\ 270^\circ+\angle\text{DOA}=360^\circ$
    $\Rightarrow\ \angle\text{DOA}=360^\circ-270^\circ=90^\circ$
    Now,
    $\angle\text{DOA}+\angle\text{AOC}=180^\circ$
    $\Rightarrow\ \angle\text{AOC}=180^\circ-90^\circ=90^\circ$

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