Question
In a $\triangle\text{ABC},$ if $\angle\text{A}=120^\circ$ and $\text{AB}=\text{AC}.$ Find $\angle\text{A}$ and $\angle\text{C}.$
✓
Answer
Consider a $\triangle\text{ABC}.$
Given Mat $\angle\text{A}=120^\circ$ and $\text{AB}=\text{AC}$ and given to find $\angle\text{B}$ and $\angle\text{C}.$
We can observe that $\triangle\text{ABC}$ is an isosceles triangle since $\text{AB}=\text{AC}$
$\angle\text{B}=\angle\text{C}$ $(i)$ [Angles opposite to equal sides are equal]
We know that sum of angles in a triangle is equal to $180^\circ $
$\Rightarrow\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
$\Rightarrow\angle\text{A}+\angle\text{B}+\angle\text{B}=180^\circ$
$\Rightarrow120^\circ+2\angle\text{B}=180^\circ$
$\Rightarrow2\angle\text{B}=180^\circ-120^\circ$
$\Rightarrow\angle\text{B}=\angle\text{C}=30^\circ$
Given Mat $\angle\text{A}=120^\circ$ and $\text{AB}=\text{AC}$ and given to find $\angle\text{B}$ and $\angle\text{C}.$
We can observe that $\triangle\text{ABC}$ is an isosceles triangle since $\text{AB}=\text{AC}$
$\angle\text{B}=\angle\text{C}$ $(i)$ [Angles opposite to equal sides are equal]
We know that sum of angles in a triangle is equal to $180^\circ $
$\Rightarrow\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
$\Rightarrow\angle\text{A}+\angle\text{B}+\angle\text{B}=180^\circ$
$\Rightarrow120^\circ+2\angle\text{B}=180^\circ$
$\Rightarrow2\angle\text{B}=180^\circ-120^\circ$
$\Rightarrow\angle\text{B}=\angle\text{C}=30^\circ$
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