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Lines and Angles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsLines and Angles1 Mark
MCQ
In the given figure, $\angle\text{BAC}=30^\circ,\angle\text{ABC}=50^\circ$ and $\angle\text{CDE}=40^\circ.$ Then $\angle\text{AED}=?$
  • ✓
    $120^\circ$
  • B
    $110^\circ$
  • C
    $80^\circ$
  • D
    $100^\circ$
✓

Answer

Correct option: A.
$120^\circ$
In $\triangle\text{ABC}$
$\angle\text{ABC}+\angle\text{BAC}+\angle\text{BCA}=180^\circ$ (Angle sum property)
$50^\circ+30^\circ+\angle\text{BCA}=180^\circ$
$\angle\text{BCA}=100^\circ$
In $\triangle\text{ECD}$
$\angle\text{ECD}+\angle\text{CDE}+\angle\text{CED}=180^\circ$ (Angle sum property)
$180^\circ-\angle\text{BCA}+40^\circ+\angle\text{CED}=180^\circ$
$\angle\text{CED}=100^\circ-40^\circ=60^\circ$
$\angle\text{CED}+\angle\text{AED}=180^\circ$ (Linear Pair)
$\angle\text{AED}=180^\circ-60^\circ=120^\circ.$

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