Question

Find the measure of each angle.

The measures of the angles of a triangle are in the ratio$3:4:5$.

Short answer

The measure of each angle is${45}^{\circ },{60}^{\circ }$ and${75}^{\circ }$ .

Step-by-step solution

Step 1. Given information.

The ratio between angles of a triangle is,

$3:4:5$

Step 2. Concept used.

The sum of angles of a triangle is${180}^{\circ }$

Since, ratio of the angles is always in the simplified form,

it might not represent the actual measure.

Step 3. Consider the angles as3x,4x, and5x .

The sum of the angles of the triangle can be expressed using the above relation as,

$\begin{array}{c}3x+4x+5x=180\\ 12x=180\\ x=15\end{array}$

So each of the angles are given by,

$\begin{array}{c}3x=3\times 15\\ 3x=45\\ 4x=4\times 15\\ 4x=60\end{array}$

And,

$\begin{array}{c}5x=5\times 15\\ 5x=75\end{array}$

Therefore, the measure of each angle is ${45}^{\circ },{60}^{\circ }$and${75}^{\circ }$.