Question
Two angles of a triangle are $30^{\circ}$ and $80^{\circ}$. Find the third angle.
✓
Answer
Let the third angle be $x$.
Then, by angle sum property of a triangle,
$
\begin{array}{c}
x+30^{\circ}+80^{\circ}=180^{\circ} \Rightarrow x+110^{\circ}=180^{\circ} \\
\Rightarrow \quad x=180^{\circ}-110^{\circ}=70^{\circ}
\end{array}
$
Hence, the third angle is $70^{\circ}$.
Then, by angle sum property of a triangle,
$
\begin{array}{c}
x+30^{\circ}+80^{\circ}=180^{\circ} \Rightarrow x+110^{\circ}=180^{\circ} \\
\Rightarrow \quad x=180^{\circ}-110^{\circ}=70^{\circ}
\end{array}
$
Hence, the third angle is $70^{\circ}$.
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