MCQ
In a $\triangle\text{ABC},$ if $\text{AB}=\text{AC}$ and $BC$ is produced to $D$ such that $\angle\text{ACD}=100^\circ$ then $\angle\text{A}=$
- ✓$20^\circ$
- B$40^\circ$
- C$60^\circ$
- D$80^\circ$
✓
Answer
Correct option: A.
$20^\circ$
$\text{AB}=\text{AC}$
$\Rightarrow\angle\text{ABC}=\angle\text{ACB} \ ($Isoscles $\triangle$ Property$)$
$\angle\text{ACB}=180^\circ-100^\circ=80^\circ$
$\Rightarrow\angle\text{ABC}-=\angle\text{ACB}=80^\circ$
$\angle\text{A}=180^\circ-\angle\text{ACB}-\angle\text{ABC}$
$=180^\circ-80^\circ-80^\circ=20^\circ$
Hence, correct option is $(a)$.
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