Question

The angles of a triangle are in the ratio $4:5:6$, find their measures in degrees

Answer 1

Step 1 : From the given ratio make angles in the form of a variable.

Whenever the ratio, to find the actual values we take a multiplier and multiply it with all the parts of the ratio, Let the multiplier be $x$

So the three angles of the triangle can be written in the as $4x,5xand6x$

Step 2 : Apply angle sum property.

$$\begin{gathered} 4x+5x+6x=180° \\ 15x=180° \\ x=\frac{180°}{15} \\ x=12° \end{gathered}$$

Step 3 : Now find the all the three angles by putting the value of $x$.

First Angle $4x=4\left(12\right)=48°$

Second Angle $5x=5\left(12\right)=60°$

Third Angle $6x=6\left(12\right)=72°$

Hence the three angles are of $48°,60°and72°$