Question
In $\triangle\text{ABC},$ if $\angle\text{A}+\angle\text{B}=125^\circ$ and $\angle\text{A}+\angle\text{C}=113^\circ,$ find $\angle\text{A},\angle\text{B}$ and $\angle\text{C}.$
✓
Answer
Since. $\angle\text{A},\angle\text{B}$ and $\angle\text{C}$ are the angles of a triangle . So, $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$ Now, $\angle\text{A}+\angle\text{B}=125^\circ$ [Given] $\therefore125^\circ+\angle\text{C}=180^\circ$
$\Rightarrow\angle\text{C}=180^\circ=125^\circ=55^\circ$ Also, $\angle\text{A}+\angle\text{C}=113^\circ$ [Given] $\Rightarrow\angle\text{A}+55^\circ=113^\circ$
$\Rightarrow\angle\text{A}=113^\circ-55^\circ=58 ^\circ$ Now as $\angle\text{A}+\angle\text{B}=125^\circ$
$\Rightarrow58^\circ+\angle\text{B}=125^\circ$
$\Rightarrow\angle\text{B}=125^\circ-58^\circ=67^\circ$
$\therefore\angle\text{A}=58^\circ,\angle\text{B}=67^\circ$ and $\angle\text{C}=55^\circ.$
$\Rightarrow\angle\text{C}=180^\circ=125^\circ=55^\circ$ Also, $\angle\text{A}+\angle\text{C}=113^\circ$ [Given] $\Rightarrow\angle\text{A}+55^\circ=113^\circ$
$\Rightarrow\angle\text{A}=113^\circ-55^\circ=58 ^\circ$ Now as $\angle\text{A}+\angle\text{B}=125^\circ$
$\Rightarrow58^\circ+\angle\text{B}=125^\circ$
$\Rightarrow\angle\text{B}=125^\circ-58^\circ=67^\circ$
$\therefore\angle\text{A}=58^\circ,\angle\text{B}=67^\circ$ and $\angle\text{C}=55^\circ.$
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