Question

The three angles of a triangle are in the ratio of $3:8:4$. Find the measure of each angle.

Answer 1

Step 1: Find the value of $x$, if the measure of the three angles of the triangle is $3x$, $8x$ and $4x$, respectively.

The sum of the measure of angles of a triangle $=180°$ [ angle sum property of triangles ]

$\Rightarrow$ $3x+8x+4x=180°$

$\Rightarrow$ $15x=180°$

$\Rightarrow$ $x=\frac{180°}{15}$

$\Rightarrow$ $x=12$

Step 2: Find the value of $3x$, $8x$ and $4x$

If $x=12$, $3x=3\times 12$

$\Rightarrow$ $3x=36$

Similarly, $8x=8\times 12$

$\Rightarrow$ $8x=96$

Also, $4x=4\times 12$

$\Rightarrow$ $4x=48$

Hence, the measure of the three angles of the triangle is $36°$, $96°$ and $48°$.