Question

The ratio of the angles of a triangle is 5:2/3:1. what are the measures of all three angles​

Answer 1

The ratio of the angles of a triangle is 5: 2/3: 1 Then the measure of all three angles are 135, 18, 27 respectively.

Solution:

Given that, the ratio of the angles of a triangle is $5: \frac{2}{3}: 1$

We have to find what are the measures of all three angles.

Let us suppose, "x" is the highest common factor of three angles.

Then, the three angles will be $5x, \frac{2}{3}x, x$

Now, we know that, sum of angles of a triangle equals to 180

$\text { Then, } 5 x+\frac{2}{3} x+x=180$

$\begin{array}{ll}{\rightarrow} & {6 x+\frac{2}{3} x=180} \\\\ {\Rightarrow} & {x\left(6+\frac{2}{3}\right)=180} \\\\ {\Rightarrow} & {x\left(\frac{6 \times 3+2}{3}\right)=180} \\\\ {\Rightarrow} & {x\left(\frac{18+2}{3}\right)=180} \\\\ {\Rightarrow} & {x \times \frac{20}{3}=180} \\\\ {\Rightarrow} & {x=180 \times \frac{3}{20}} \\\\ {\Rightarrow} & {x=9 \times 3=27}\end{array}$

So, the three angles will be,

$5x = 5 \times 27 = 135\\\\\frac{2}{3} \times 27 = 18\\\\x = 27$

Hence, the angles of the triangle are 135, 18, 27 respectively.