MCQ
If $\triangle\text{ABC}$ is an isosceles triangle with A$B = AC$ and $\angle\text{B} = 65^\circ,$ find $\angle\text{A}.$
- A$70^\circ$
- ✓$50^\circ$
- C$60^\circ$
- DNone of these
✓
Answer
Correct option: B.
$50^\circ$
In isosceles triangle $ABC$
$AB = AC$ (Given)
Therefore $\angle\text{B} = \angle\text{C} = 65^\circ$ (angles opposite to equal side are equal).
So, by applying angle sum property i.e $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ,$
$\angle\text{A} + 65^\circ + 65^\circ = 180^\circ$
$\angle\text{A} = 180^\circ - 130^\circ$
$\angle\text{A} = 50^\circ$
$AB = AC$ (Given)
Therefore $\angle\text{B} = \angle\text{C} = 65^\circ$ (angles opposite to equal side are equal).
So, by applying angle sum property i.e $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ,$
$\angle\text{A} + 65^\circ + 65^\circ = 180^\circ$
$\angle\text{A} = 180^\circ - 130^\circ$
$\angle\text{A} = 50^\circ$
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