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: (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, (2)/(3)x, x`

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

`\text { Then, } 5 x+(2)/(3) x+x=180`

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

So, the three angles will be,

`5x = 5 * 27 = 135\\\\(2)/(3) * 27 = 18\\\\x = 27`

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