Question
If the angles of a triangle are in the ratio $1 : 2 : 3$, determine three angles.
✓
Answer
Given Data: Angles of a triangle are in the ratio $1: 2: 3$ Let the angles be $x, 2x, 3x$.
$\therefore$ We know that, Sum of all angles of triangles is $180^\circ $ $\text{x}+2\text{x}+3\text{x}=180^\circ$
$\Rightarrow6\text{x}=180^\circ$
$\Rightarrow\text{x}=\frac{180^\circ}{6}$
$\Rightarrow\text{x}=30^\circ$
Since $\text{x}=30^\circ$ $2x = 2(30)^\circ = 60^\circ\ 3x = 3(30)^\circ = 90^\circ $
Therefore, angles are $30^\circ , 60^\circ , 90^\circ $.
$\therefore$ We know that, Sum of all angles of triangles is $180^\circ $ $\text{x}+2\text{x}+3\text{x}=180^\circ$
$\Rightarrow6\text{x}=180^\circ$
$\Rightarrow\text{x}=\frac{180^\circ}{6}$
$\Rightarrow\text{x}=30^\circ$
Since $\text{x}=30^\circ$ $2x = 2(30)^\circ = 60^\circ\ 3x = 3(30)^\circ = 90^\circ $
Therefore, angles are $30^\circ , 60^\circ , 90^\circ $.
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