Question
In a $\triangle\text{ABC},$ if $\text{AB}=\text{AC}$ and $\angle\text{B}=70^\circ.$ Find $\angle\text{A}.$
✓
Answer
In a $\triangle\text{ABC},$ if $\text{AB}=\text{AC}$ and $\angle\text{B}=70^\circ$
Since, $\text{AB}=\text{AC }\triangle\text{ABC}$ is an isosceles triangle
$\angle\text{B}=\angle\text{C}$ [Angles opposite to equal sides are equal]
$\angle\text{B}=\angle\text{C}=70^\circ$ And
also, Sum of angles in a triangle $= 180^\circ$
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
$\angle\text{A}+70^\circ+70^\circ=180^\circ$
$\angle\text{A}=180^\circ-140^\circ$
$\angle\text{A}=40^\circ$
Since, $\text{AB}=\text{AC }\triangle\text{ABC}$ is an isosceles triangle
$\angle\text{B}=\angle\text{C}$ [Angles opposite to equal sides are equal]
$\angle\text{B}=\angle\text{C}=70^\circ$ And
also, Sum of angles in a triangle $= 180^\circ$
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
$\angle\text{A}+70^\circ+70^\circ=180^\circ$
$\angle\text{A}=180^\circ-140^\circ$
$\angle\text{A}=40^\circ$
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